JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) be the solution of the differential equation \(2 \cos x \frac{\mathrm{~d} y}{\mathrm{~d} x}=\sin 2 x-4 y \sin x, x \in\left(0, \frac{\pi}{2}\right)\). If \(y\left(\frac{\pi}{3}\right)=0\), then \(y^{\prime}\left(\frac{\pi}{4}\right)+y\left(\frac{\pi}{4}\right)\) is equal to ________.
- A 1
- B 2
- C 3
- D 4
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \frac{d y}{d x}+2 y \tan x=\sin x \\ & \text { I.F. }=e^{2 \int \tan x d x}=\sec ^2 x \\ & y \sec ^2 x=\int \frac{\sin x}{\cos ^2 x} d x \\ & =\int \tan x \sec x d x \\ & =\sec x+C \\ & C=-2\end{aligned}\)…
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