JEE Mains · Maths · STD 12 - 9. differential equations
If \(y=y(x), y \in\left[0, \frac{\pi}{2}\right)\) is the solution of the differential equation \(\sec y \frac{d y}{d x}-\sin (x+y)-\sin (x-y)=\) 0, with \(y(0)=0\), then \(5 y^{\prime}\left(\frac{\pi}{2}\right)\) is equal to \(......\)
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(\sec y \frac{d y}{d x}=2 \sin x \cos y\) \(\sec ^{2} y d y=2 \sin x d x\) \(\tan y=-2 \cos x+c\) \(c=2\) \(\tan y=-2 \cos x+2 \Rightarrow \text { at } x=\frac{\pi}{2}\) \(\tan y=2\) \(\sec ^{2} y \frac{d y}{d x}=2 \sin x\) \(5 \frac{d y}{d x}=2\)
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