JEE Mains · Maths · STD 12 - 9. differential equations
If \(\frac{{dy}}{{dx}} + y\tan x = \sin 2x\) and \(y(0)\,=1\) , then \(y(\pi)\) is equal to
- A \(1\)
- B \(-1\)
- C \(-5\)
- D \(5\)
Answer & Solution
Correct Answer
(C) \(-5\)
Step-by-step Solution
Detailed explanation
Let \(\frac{d y}{d x}+y \tan x=\sin 2 x\) \(\mathrm{IF}=e^{\int \tan x d x}=e^{-\log \cos x}=\sec x\) Required solution is \(y(\sec x)=\int \sin 2 x \sec x d x+c\) \(y(\sec x)=\int \frac{2 \sin x \cos x}{\cos x} d x+c\) \(y(\sec x)=2 \int \sin x d x+c\) \(y(\sec x)=-2 \cos x+c\)…
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