Q.For each of the differential equations given below, indicate its order and degree (if defined).

Showing the 12 most recent of 26 on this concept.

1. AP EAPCET 2026Set eng-2026-05-15-FN1 markMCQ
   Q.Among the following the differential equations, the equation having order 2 and degree 3 is (A) $\dfrac{dy}{dx} - \sin y = \dfrac{d^2y}{dx^2}\left(\sqrt{\dfrac{d^2y}{dx^2} - 1}\right)$ (B) $\left(\dfrac{d^2y}{dx^2}\right)^3 = \dfrac{dy}{dx} + y^2\left(\dfrac{d^3y}{dx^3}\right)^2$ (C) $\left(\dfrac{d^2y}{dx^2}\right)^3 = \left(\dfrac{d^2y}{dx^2}\right)^{3/2} + x^2$ (D) $\dfrac{dy}{dx} - \sin y = \left(\dfrac{d^2y}{dx^2}\right)^3\left(\sqrt{\dfrac{d^2y}{dx^2}} - 1\right)$

   ›Reveal solutionSolution

   Order is the highest derivative present; degree is the power of that highest derivative once the equation is made free of radicals/fractional powers involving derivatives. Only option (A) reduces to order 2, degree 3. Answer: (A).

   Concept and Intuition

   To find the degree of a differential equation, first make sure it is written as a polynomial in derivatives — any square roots, fractional powers, or derivatives inside denominators must be cleared first (by squaring, cubing, etc., as needed) before reading off the exponent of the highest-order derivative term.

   Step-by-Step Solution

   1. Option (A): $\dfrac{dy}{dx}-\sin y=y''\sqrt{y''-1}$. Highest derivative: $y''$ (order 2). Isolate the radical (already isolated) and square both sides: $\left(\dfrac{dy}{dx}-\sin y\right)^2=(y'')^2(y''-1)=(y'')^3-(y'')^2$. This is polynomial in $y''$ with highest power $3$ — order 2, degree 3. ✓ Matches what's asked.
   2. Option (B): $(y'')^3=y'+y^2(y''')^2$. Highest derivative is $y'''$ (order 3), appearing squared — order 3, degree 2. Does not match.
   3. Option (C): $(y'')^3=(y'')^{3/2}+x^2$. Isolate the fractional power: $(y'')^3-x^2=(y'')^{3/2}$; squaring: $\left[(y'')^3-x^2\right]^2=(y'')^3$, giving highest power $(y'')^6$ — order 2, degree 6. Does not match.
   4. Option (D): $\dfrac{dy}{dx}-\sin y=(y'')^3(\sqrt{y''}-1)=(y'')^{7/2}-(y'')^3$. Isolating and squaring gives a degree of 7 in $y''$ — order 2, degree 7. Does not match.
   5. Only (A) gives the required order 2, degree 3.

   Common Mistakes

   • Reading off the degree directly from the exponent of the outer term (e.g. treating the exponent "3" in $y''\sqrt{y''-1}$ literally) without actually clearing the radical first.
   • Confusing order (which derivative is highest) with degree (its power).

   ✓Final answer

   The correct option is (A) — $\dfrac{dy}{dx} - \sin y = \dfrac{d^2y}{dx^2}\left(\sqrt{\dfrac{d^2y}{dx^2} - 1}\right)$.

   ANSWER: A

2. AP EAPCET 2022Set eng-2022-07-07-AN1 markMCQ
   Q.If a and b are respectively the order and degree of a differential equation $y^2(y'')^2 + 3x(y')^{1/3} + x^2y^2 = \sin x$, then (A) $b = a$ (B) $a = 3b$ (C) $b = 3a$ (D) $ab = 6$

   ›Reveal solutionSolution

   Order is fixed by the highest derivative ($y''$, so $a=2$); clearing the fractional power on $y'$ by cubing the whole equation raises the power of $y''$ to $6=3a$, giving $b=3a$.

   Concept and Intuition

   The order of a differential equation is simply the order of the highest derivative appearing. The degree is only defined once the equation is written as a polynomial in all the derivatives (integer, non-negative powers) — so any fractional or negative power on a derivative must first be cleared by an appropriate algebraic operation (like raising both sides to a power), and this operation can also change the power of other derivative terms present in the equation.

   Step-by-Step Solution

   1. The equation is $y^2(y'')^2+3x(y')^{1/3}+x^2y^2=\sin x$.
   2. The highest-order derivative present is $y''$ (second derivative), so the order $a=2$.
   3. The term $(y')^{1/3}$ has a fractional exponent, so the equation is not yet a polynomial in the derivatives.
   4. Isolate that term: $3x(y')^{1/3} = \sin x - y^2(y'')^2 - x^2y^2$.
   5. Cube both sides to clear the cube root: $27x^3(y') = \big[\sin x - y^2(y'')^2-x^2y^2\big]^3$.
   6. Expanding the cube, the term with the highest power of $y''$ comes from cubing $-y^2(y'')^2$ alone, giving $-y^6(y'')^6$ — so $y''$ now appears to the power $6$.
   7. Hence the degree is $b=6$.
   8. Compare with $a=2$: $b=3a$ since $3\times2=6$.

   Common Mistakes

   • Reading off the exponent $2$ on $(y'')^2$ directly as the degree, without first checking whether the equation is already a polynomial in all derivatives (it isn't, because of the fractional-power $y'$ term).
   • Forgetting that clearing one derivative's fractional power (via cubing the whole equation) also multiplies the exponent of every other derivative term by the same factor.

   ✓Final answer

   The correct option is (C) — $b = 3a$.

   ANSWER: C

3. AP EAPCET 2024Set eng-2024-05-19-AN1 markMCQ
   Q.The difference of the order and degree of the differential equation $\left(\dfrac{d^2y}{dx^2}\right)^{-7/2}\left(\dfrac{d^3y}{dx^3}\right)^2-\left(\dfrac{d^2y}{dx^2}\right)^{-5/2}\left(\dfrac{d^4y}{dx^4}\right)=0$ is (A) $5$ (B) $3$ (C) $4$ (D) $2$

   ›Reveal solutionSolution

   Order $=4$, degree $=1$, so their difference is $4-1=3$.

   Concept and Intuition

   The order of a differential equation is the order of its highest derivative. The degree is the power of the highest-order derivative once the equation is made a polynomial in all derivatives (free of fractional/negative exponents).

   Step-by-Step Solution

   1. Highest derivative is $\dfrac{d^4y}{dx^4}$ so the order is 4.
   2. Multiply the whole equation by $\left(\dfrac{d^2y}{dx^2}\right)^{7/2}$ to remove negative fractional powers.
   3. First term: $\left(\dfrac{d^3y}{dx^3}\right)^2$; second term: $\left(\dfrac{d^2y}{dx^2}\right)^{1}\dfrac{d^4y}{dx^4}$.
   4. The equation is now polynomial, with $\dfrac{d^4y}{dx^4}$ appearing to the first power, so degree $=1$.
   5. Difference $= 4-1 = 3$.

   Common Mistakes

   • Reading degree directly from the fractional exponents without first clearing them.
   • Taking the power $2$ on $d^3y/dx^3$ as the degree — degree refers to the highest-order derivative.

   ✓Final answer

   The correct option is (B) — $3$.

   ANSWER: B

   Note

   This solution was worked out by our team and cross-checked by a second independent solve. The official answer key for this question could not be confirmed, so please cross-verify with the official paper where possible.

4. AP EAPCET 2023Set eng-2023-05-17-AN1 markMCQ
   Q.The order and degree of the differential equation $3x^2\dfrac{d^2y}{dx^2}-\sin\left(\dfrac{d^3y}{dx^3}\right)+\cos(xy)=0$ are (A) Order can't be defined and degree is 3 (B) Order is 3 and degree can't be defined (C) Order is 3 and degree is 1 (D) Order is 1 and degree is 3

   ›Reveal solutionSolution

   Because the highest derivative $y'''$ sits inside a $\sin(\cdot)$, the equation is not a polynomial in derivatives, so its degree is undefined even though its order (3) is perfectly well defined.

   Concept and Intuition

   Order of a DE = order of the highest derivative appearing. Degree = the power of the highest-order derivative, but this is only defined when the equation, after clearing radicals/fractions, is a polynomial in all the derivatives. If the highest derivative appears inside a non-polynomial function (sin, log, exponential, etc.), degree simply cannot be assigned.

   Step-by-Step Solution

   1. The DE is $3x^2y''-\sin(y''')+\cos(xy)=0$.
   2. The highest-order derivative present is $y'''$ (third derivative) — so the order is $3$.
   3. However, $y'''$ appears as the argument of $\sin(\cdot)$, not raised to an integer power — this equation is not a polynomial in $y'''$ (or any of the derivatives), even after any algebraic rearrangement, since $\sin$ cannot be turned into a finite polynomial expression in $y'''$.
   4. Therefore the degree is not defined, while the order is 3.

   Common Mistakes

   • Assuming "the coefficient of the highest derivative is 1 inside sin" makes the degree 1 — degree requires a polynomial equation, and $\sin(y''')$ is transcendental in $y'''$, not polynomial.
   • Confusing which derivative sets the order — it's $y'''$ (order 3), not $y''$.

   ✓Final answer

   The correct option is (B) — Order is 3 and degree can't be defined.

   ANSWER: B

5. AP EAPCET 2023Set eng-2023-05-15-FN1 markMCQ
   Q.The order and degree of the differential equation $\left(\dfrac{d^3y}{dx^3}\right)^{1/2} - 2\left(\dfrac{dy}{dx}\right)^{1/4} + xy = 0$ are respectively (A) 3 and 12 (B) 3 and 2 (C) 3 and 4 (D) 3 and 6

   ›Reveal solutionSolution

   The order is 3 (from the third derivative); after systematically squaring twice to clear all fractional exponents (the $1/2$ power on $y'''$ and the $1/4$ power on $y'$), the equation becomes polynomial with $y'''$ appearing to the 4th power — so degree $=4$.

   Concept and Intuition

   Order is simply the highest derivative present (here, the third derivative, so order 3). Degree requires the equation to first be made polynomial in all the derivatives (no fractional or negative powers, no derivatives inside radicals) — only then is the degree the power of the highest-order derivative. Since we have two different fractional powers ($1/2$ on $y'''$ and $1/4$ on $y'$), we must clear both, which can require squaring more than once and tracks a growing power on $y'''$.

   Step-by-Step Solution

   1. Order: the highest derivative is $\dfrac{d^3y}{dx^3}$, so order $=3$.

   2. Clearing the fractional powers — write $p=y'''$, $q=y'$, $a=xy$:

   $p^{1/2} - 2q^{1/4} + a = 0 \implies p^{1/2} = 2q^{1/4}-a$

   3. Square once to remove the $1/2$ power on $p$:

   $p = 4q^{1/2} - 4a\,q^{1/4} + a^2$

   This still carries fractional powers of $q$ (namely $q^{1/2}$ and $q^{1/4}$), which must also be cleared since all derivative terms must end up with integer powers, not just the highest one.

   4. Isolate the term with the highest remaining fractional power ($q^{1/4}$), letting $w=q^{1/4}$ (so $q^{1/2}=w^2$):

   $p - a^2 = 4w^2 - 4a\,w$

   This is a quadratic in $w$:

   $4w^2 - 4a\,w - (p-a^2) = 0 \implies w = \frac{a \pm \sqrt{p}}{2}$

   (after simplifying the quadratic formula, using $a^2+p-a^2=p$ inside the root).

   5. Raise both sides to the 4th power to remove $w=q^{1/4}$ entirely: $q = \left(\dfrac{a\pm\sqrt p}{2}\right)^4$. Expanding and isolating the remaining $\sqrt p$ term, then squaring once more to eliminate it, produces a final polynomial equation in $p$ alone (together with $a,q$) whose highest power of $p=y'''$ is 4 — arising because the expansion of the 4th power creates a $p^2$ term, and the final squaring step (needed to remove the leftover square root) doubles that to $p^4$.

   6. So after fully clearing all radicals, the equation is a polynomial of degree 4 in $y'''$, while remaining order 3 (still only third derivatives appear, no higher).

   Common Mistakes

   • Stopping after the first squaring (thinking degree $=2$) and forgetting that the other fractional power (on $y'$) must also be cleared before degree is well-defined, since the standard convention requires the whole equation to be free of fractional/negative powers of derivatives.
   • Confusing "order" (3, straightforward) with "degree" (which requires this careful algebraic clearing).

   ✓Final answer

   The correct option is (C) — 3 and 4.

   ANSWER: C

6. AP EAPCET 2023Set eng-2023-05-18-AN1 markMCQ
   Q.The degree of the differential equation $\log\left(\frac{dy}{dx}\right)=\left(2x+3\frac{dy}{dx}\right)^2$ is (A) $1$ (B) $2$ (C) $3$ (D) not defined

   ›Reveal solutionSolution

   Because the derivative sits inside a transcendental function (a logarithm) rather than as a pure power, this differential equation has no polynomial form in $dy/dx$, so its degree is not defined.

   Concept and Intuition

   The "degree" of a differential equation is defined as the power of the highest-order derivative, but ONLY after the equation has been made free of radicals, fractional powers, and any derivative sitting inside a non-polynomial (transcendental) function such as $\log$, $\sin$, $e^{(\cdot)}$, etc. If the derivative cannot be isolated as a polynomial term, degree is simply not defined — order is still defined (here order $=1$), but degree is not.

   Step-by-Step Solution

   1. The equation is $\log\!\left(\dfrac{dy}{dx}\right)=\left(2x+3\dfrac{dy}{dx}\right)^2$.
   2. The highest derivative present is $\dfrac{dy}{dx}$ (order 1), but it appears inside a $\log(\cdot)$ on the left side.
   3. There is no way to algebraically rearrange this into a polynomial equation in $\dfrac{dy}{dx}$ (the log cannot be removed without introducing an exponential of the RHS, which is not a polynomial either).
   4. Since the equation cannot be written as a polynomial in the derivatives, its degree is, by definition, not defined.

   Common Mistakes

   • Confusing "order" (which is well-defined here, $=1$) with "degree" (which is not).
   • Trying to force a degree by looking only at the exponent "2" on the RHS while ignoring that the LHS derivative sits inside a log.

   ✓Final answer

   The correct option is (D) — not defined.

   ANSWER: D

7. AP EAPCET 2024Set eng-2024-05-20-AN1 markMCQ
   Q.Order and degree of the differential equation $\dfrac{d^3y}{dx^3} = \left[1+\left(\dfrac{dy}{dx}\right)^2\right]^{5/2}$ respectively are (A) $5, 2$ (B) $3, 5$ (C) $3, 2$ (D) $2, 3$

   ›Reveal solutionSolution

   Order is the highest derivative present ($3$); degree requires clearing the fractional exponent first, which makes the highest derivative appear squared — giving order $3$, degree $2$: (C).

   Concept and Intuition

   "Order" of a differential equation is simply the order of the highest derivative appearing. "Degree" is the power of the highest-order derivative after the equation has been made a polynomial in derivatives (i.e., all fractional/negative powers of derivatives must first be cleared by algebraic manipulation such as squaring).

   Step-by-Step Solution

   1. The highest derivative present is $\dfrac{d^3y}{dx^3}$ — a third-order derivative. So order $=3$.
   2. The RHS, $\left[1+\left(\dfrac{dy}{dx}\right)^2\right]^{5/2}$, has a fractional exponent, so the equation is not yet in polynomial form.
   3. Square both sides to remove the fractional power: $\left(\dfrac{d^3y}{dx^3}\right)^2=\left[1+\left(\dfrac{dy}{dx}\right)^2\right]^5$.
   4. Now the equation is polynomial in the derivatives, and the highest-order derivative $\dfrac{d^3y}{dx^3}$ appears to the power $2$. So degree $=2$.

   Common Mistakes

   • Reading off the exponent $5/2$ directly as the "degree" — degree is only defined after clearing fractional powers, not before.
   • Confusing order (of the derivative) with degree (of the equation in that derivative).

   ✓Final answer

   The correct option is (C) — $3,\ 2$.

   ANSWER: C

8. AP EAPCET 2024Set eng-2024-05-20-FN1 markMCQ
   Q.The sum of the order and degree of the differential equation $\dfrac{d^4y}{dx^4}=\left\{c+\left(\dfrac{dy}{dx}\right)^2\right\}^{3/2}$ is (A) $4$ (B) $6$ (C) $5$ (D) $8$

   ›Reveal solutionSolution

   Squaring both sides clears the $3/2$ power, giving order $4$ and degree $2$; their sum is $6$.

   Concept and Intuition

   Degree is only meaningful once the differential equation is written as a polynomial in all the derivatives involved — any radicals (fractional powers) on a derivative term must first be removed by an algebraic operation such as squaring, cubing, etc.

   Step-by-Step Solution

   1. Given: $\dfrac{d^4y}{dx^4}=\left\{c+\left(\dfrac{dy}{dx}\right)^2\right\}^{3/2}$.
   2. Square both sides to remove the $3/2$ power: $\left(\dfrac{d^4y}{dx^4}\right)^2 =\left\{c+\left(\dfrac{dy}{dx}\right)^2\right\}^3$.
   3. This is now a genuine polynomial equation in the derivatives $y''''$ and $y'$.
   4. Highest-order derivative: $y''''=\dfrac{d^4y}{dx^4}$, so order $=4$.
   5. That highest-order derivative appears with power $2$ on the left, so degree $=2$.
   6. Sum of order and degree $=4+2=6$.

   Common Mistakes

   • Reading the degree straight off the un-squared equation as $3/2$ (degree must be a whole number, obtained only after clearing radicals).
   • Miscounting the order as $1$ by focusing on the $dy/dx$ term instead of the highest derivative $y''''$.

   ✓Final answer

   The correct option is (B) — $6$.

   ANSWER: B

9. AP EAPCET 2021Set eng-2021-08-23-FN1 markMCQ
   Q.The order and degree of the differential equation $\sqrt{\dfrac{dy}{dx}} - 4\dfrac{dy}{dx} - 7x = 0$ are respectively ______ (A) $1$ & $\dfrac{1}{2}$ (B) $2$ & $1$ (C) $1$ & $1$ (D) $1$ & $2$

   ›Reveal solutionSolution

   Order is the highest derivative present; degree is the power of the highest derivative once the equation is rationalized (radical-free) in the derivatives.

   Concept and Intuition

   The order of a differential equation is simply the order of the highest derivative appearing in it. The degree is only defined once the equation is a polynomial in its derivatives (no radicals or fractional powers involving a derivative) — so before reading off the degree, we must first clear any such radical by squaring or otherwise rationalizing.

   Step-by-Step Solution

   1. The equation is $\sqrt{\dfrac{dy}{dx}} - 4\dfrac{dy}{dx} - 7x = 0$.
   2. Only $dy/dx$ (first derivative) appears — no $d^2y/dx^2$ or higher — so the order is 1.
   3. To find the degree, isolate the radical: $\sqrt{\dfrac{dy}{dx}} = 4\dfrac{dy}{dx}+7x$.
   4. Square both sides to remove the square root: $\dfrac{dy}{dx} = \left(4\dfrac{dy}{dx}+7x\right)^2$.
   5. Expanding the right side gives a term $16\left(\dfrac{dy}{dx}\right)^2$, so the highest power of $dy/dx$ in this polynomial form is $2$.
   6. Hence the degree is 2.

   Common Mistakes

   • Reading the degree directly off the original (un-rationalized) equation, which would incorrectly suggest a fractional degree of $1/2$.
   • Confusing order (count of the highest derivative) with degree (its power after rationalizing).

   ✓Final answer

   The correct option is (D) — $1$ & $2$.

   ANSWER: D

10. AP EAPCET 2026Set eng-2026-05-14-AN1 markMCQ
    Q.The order and degree of the differential equation $\left\{1+\left(\dfrac{dy}{dx}\right)^2\right\}^{3/2} = \dfrac{d^2y}{dx^2}$ are respectively (A) $\dfrac{3}{2},2$ (B) $2,3$ (C) $2,2$ (D) $3,4$

    ›Reveal solutionSolution

    The order is the highest derivative present ($y''$, order $2$); the degree requires first clearing the fractional power by squaring, after which the highest derivative appears to the power $2$ — so order and degree are both $2$.

    Concept and Intuition

    The order of a differential equation is simply the order of the highest derivative appearing. The degree is the power of the highest-order derivative after the equation has been made a polynomial in all the derivatives (no fractional or negative powers of any derivative allowed) — so if a fractional power like $3/2$ appears on an expression containing lower derivatives, you must algebraically clear it before reading off the degree.

    Step-by-Step Solution

    1. The equation is $\left\{1+\left(\dfrac{dy}{dx}\right)^2\right\}^{3/2}=\dfrac{d^2y}{dx^2}$.
    2. The highest derivative present is $\dfrac{d^2y}{dx^2}$ — so the order is 2.
    3. The left side has a fractional exponent $3/2$ on an expression involving $dy/dx$ (not the highest derivative), so we cannot read the degree directly; we must eliminate the fractional power.
    4. Square both sides: $\left\{1+\left(\dfrac{dy}{dx}\right)^2\right\}^{3}=\left(\dfrac{d^2y}{dx^2}\right)^{2}$.
    5. Now the equation is polynomial in all derivatives, and the highest-order derivative $d^2y/dx^2$ appears with power $2$ — so the degree is 2.

    Common Mistakes

    • Reading off "degree $3/2$" directly from the unsquared equation — degree must always be a positive integer, which is the signal that the equation needs to be rationalized first.
    • Confusing order (highest derivative present) with degree (power of the highest derivative after rationalizing).

    ✓Final answer

    The correct option is (C) — $2,2$.

    ANSWER: C

11. AP EAPCET 2023Set eng-2023-05-17-AN1 markMCQ
    Q.Let $c_1,c_2,c_3,c_4$ be arbitrary constants. The order of the differential equation, corresponding to $y=c_1e^x+c_2e^{\log_e x}+c_3\sin^2 x-c_4(\cos^2 x-1)$ is (A) 1 (B) 2 (C) 3 (D) 4

    ›Reveal solutionSolution

    Simplifying the given expression shows $c_3$ and $c_4$ always appear only as the sum $c_3+c_4$, so there are really just 3 independent arbitrary constants, making the order of the corresponding DE equal to 3.

    Concept and Intuition

    The order of the differential equation satisfied by a family of curves equals the number of independent arbitrary constants in the family — not simply the number of symbols written. Redundant constants (ones that only ever appear combined) must be collapsed first.

    Step-by-Step Solution

    1. Simplify $e^{\log_e x}=x$ (for $x>0$).
    2. Simplify $-c_4(\cos^2x-1)=-c_4(-\sin^2x)=c_4\sin^2x$.
    3. So $y=c_1e^x+c_2x+c_3\sin^2x+c_4\sin^2x=c_1e^x+c_2x+(c_3+c_4)\sin^2x$.
    4. Let $C_3=c_3+c_4$ — a single arbitrary constant (since $c_3,c_4$ are both arbitrary, their sum is just another arbitrary constant, with no independent extra freedom).
    5. So the family is effectively $y=c_1e^x+c_2x+C_3\sin^2x$ — exactly 3 independent arbitrary constants.
    6. Hence the order of the differential equation representing this family is 3.

    Common Mistakes

    • Counting 4 constants at face value without noticing $c_3,c_4$ collapse into one.
    • Forgetting to simplify $e^{\log_e x}$ to $x$ first, which could obscure the constant-counting.

    ✓Final answer

    The correct option is (C) — 3.

    ANSWER: C

12. AP EAPCET 2024Set eng-2024-05-22-FN1 markMCQ
    Q.The sum of the order and degree of the differential equation $x\left(\dfrac{d^2y}{dx^2}\right)^{1/2} = \left(1 + \dfrac{dy}{dx}\right)^{4/3}$ is (A) $5$ (B) $8$ (C) $12$ (D) $10$

    ›Reveal solutionSolution

    Order and degree are only meaningful after the equation is made polynomial in its derivatives — that requires clearing the fractional exponents first. Answer: $5$.

    Concept and Intuition

    The order of a differential equation is the order of the highest derivative present. The degree is the power of the highest-order derivative, but only after the equation has been rewritten as a polynomial in the derivatives (no fractional or negative powers of any derivative term). So before reading off the degree, any radicals or fractional exponents on derivative terms must be cleared.

    Step-by-Step Solution

    1. Given: $x\left(\dfrac{d^2y}{dx^2}\right)^{1/2} = \left(1+\dfrac{dy}{dx}\right)^{4/3}$.
    2. The highest derivative present is $y''=\dfrac{d^2y}{dx^2}$, so the order is $2$.
    3. To clear the fractional powers $\tfrac12$ and $\tfrac43$, raise both sides to the power $6$ (the LCM of denominators $2$ and $3$): $x^6(y'')^3 = (1+y')^8.$
    4. Now the equation is polynomial in derivatives, and the highest-order derivative $y''$ appears to the power $3$ — so the degree is $3$.
    5. Sum of order and degree: $2+3=5$.

    Common Mistakes

    • Reading off the degree directly from the un-cleared equation (e.g., taking the exponent $1/2$ as the "degree"), which is invalid since degree must be a non-negative integer from a polynomial form.
    • Using an incorrect LCM (e.g., raising to the 3rd or 2nd power alone) and failing to fully clear both fractional exponents simultaneously.

    ✓Final answer

    The correct option is (A) — $5$.

    ANSWER: A