The solution of $\frac{dy}{dx} = 1$ is ______. (a) $x + y = c$ (b) $xy = c$ (c) $x^2 + y^2 = c$ (d) $y - x = c$

The solution of (dy)/(dx) = 1 is ___. (a) x + y = – Class 12 Mathematics And Statistics

Question 37 of 40

\frac{dy}{dx} = 1

(a)

x + y = c

(b)

xy = c

(c)

x^2 + y^2 = c

(d)

y - x = c

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Integrate $\dfrac{dy}{dx}=1$ directly to get $y = x + c$ , i.e. $y - x = c$ — option (iv).

The equation is already in variables-separable form:

$\frac{dy}{dx} = 1 \;\Rightarrow\; dy = dx.$

Integrating both sides:

$\int dy = \int dx \;\Rightarrow\; y = x + c,$

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