Reduce to variable separable form and solve: $\cos^2(x-2y)=1-2\dfrac{dy}{dx}$

Reduce to variable separable form and solve: cos²(x-2y)=1-2(dy)/(dx)

Exercise 6.3 · Q52

\cos^2(x-2y)=1-2\dfrac{dy}{dx}

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★

29% · 52/177 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

Put $u=x-2y$ , so $\dfrac{du}{dx}=1-2\dfrac{dy}{dx}$ . The equation $\cos^2(x-2y)=1-2\dfrac{dy}{dx}$ becomes $\cos^2u=\dfrac{du}{dx}$ , i.e. $\sec^2u\,du=dx$ . Integr …

Start your 14-day free trial to unlock the full solution →

Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2024Set ANNUAL2 marks
$1+\dfrac{dy}{dx}=\csc(x+y)$
›Reveal solutionSolution

Put $u=x+y$ ; the equation becomes $\dfrac{du}{dx}=\csc u$ , separable.

$u=x+y \Rightarrow \dfrac{du}{dx}=1+\dfrac{dy}{dx}=\csc u$

$\sin u\,du=dx$

…

Start your 14-day free trial to see the full solution →
CBSE 2023Set ANNUAL2 marksMCQ
$\dfrac{dx}{dt} = \dfrac{x\log x}{t}$
(a) $x = e^{ct}$
(b) $x + e^{ct} = 0$
(c) $x = e^t + t$
(d) $xe^{ct} = 0$
›Reveal solutionSolution

Separate variables and integrate.

$\dfrac{dx}{x\log x}=\dfrac{dt}{t}$

Integrating: $\log(\log x)=\log t+\log k=\log(kt)$

…

Start your 14-day free trial to see the full solution →
CBSE 2023Set ANNUAL2 marks
$\cos x \cos y\,dy - \sin x \sin y\,dx = 0$
›Reveal solutionSolution

Separate variables: $\cot y\,dy=\tan x\,dx$ .

$\cos x\cos y\,dy=\sin x\sin y\,dx \Rightarrow \cot y\,dy=\tan x\,dx$

Integrating: $\log|\sin y|=-\log|\cos x|+\log k$

…

Start your 14-day free trial to see the full solution →
CBSE 2022Set ANNUAL2 marks
$y\dfrac{dy}{dx} + x = 0$
›Reveal solutionSolution

Separate variables and integrate.

$y\dfrac{dy}{dx}+x=0 \implies y\,dy = -x\,dx$

…

Start your 14-day free trial to see the full solution →
CBSE 2020Set ANNUAL2 marks
$\dfrac{dy}{dx} = x^2y + y$
›Reveal solutionSolution

Separate variables and integrate.

$\dfrac{dy}{dx} = y(x^2+1)$

Separating variables:

$\dfrac{dy}{y} = (x^2+1)\,dx$

Integrating both sides: …

Start your 14-day free trial to see the full solution →

←Previous question · 6.3Q51 — Reduce to variable separable form and solve: x+y(dy)/(dx)=sec(x²+y²)→Next question · 6.3Q53 — Reduce to variable separable form and solve: (2x-2y+3)dx-(x-y+1)dy=0, …

Q.Reduce to variable separable form and solve: $\cos^2(x-2y)=1-2\dfrac{dy}{dx}$

Concept understanding — Differential Equations with Variables Separable

Q.Reduce to variable separable form and solve: cos⁡2(x−2y)=1−2dydx\cos^2(x-2y)=1-2\dfrac{dy}{dx}cos2(x−2y)=1−2dxdy​

🎓Unlock everything free for 14 days

Q.Reduce to variable separable form and solve: $\cos^2(x-2y)=1-2\dfrac{dy}{dx}$

Unlock everything free for 14 days