A function y=f(x) satisfies f(x) sin 2 x+sin x- (1+cos 2 x ) f prime (x)=0 with condition f(0)=0 . Then f (π/2 ) is equal to

Mathematics · Differential Equations

JEE Main 2024 — 29 January, Shift 1 — Question 11

A function $y=f(x)$ satisfies $f(x) \sin 2 x+\sin x-\left(1+\cos ^{2} x\right) f^{\prime}(x)=0$ with condition $f(0)=0$ . Then $f\left(\frac{\pi}{2}\right)$ is equal to

Option A:
1
Correct
Option B:
0
Option C:
-1
Option D:
2

Answer: A

Step-by-step solution

$\frac{d y}{d x}-\left(\frac{\sin 2 x}{1+\cos ^{2} x}\right) y=\sin x$

I.F. $=1+\cos ^{2} x$

$y \cdot\left(1+\cos ^{2} x\right)=\int(\sin x) d x$

$=-\cos x+C$

$\mathrm{x}=0, \mathrm{C}=1$

$\mathrm{y}\left(\frac{\pi}{2}\right)=1$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 29 January, Shift 1
Subject: Mathematics
Chapter: Differential Equations
Topic: Methods of solving a First Order,First Degree Differential

If the solution curve y=y(x) of the differential equation (1+y^2 ) (1+log e x ) d x+x d y=0, x 0 passes through the point (1,1) and…

Answer: A

Step-by-step solution

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