JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) be the solution curve of the differential equation secy \(\frac{d y}{d x}+2 x \sin y=x^3 \cos y\), \(y(1)=0\). Then \(y(\sqrt{3})\) is equal to :
- A \(\frac{\pi}{3}\)
- B \(\frac{\pi}{6}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{12}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\( \sec ^2 y \frac{d y}{d x}+2 x \sin y \text { secy }=x^3 \cos y \text { secy } \) \( \sec ^2 y \frac{d y}{d x}+2 x \tan y=x^3 \) \( \tan y=t \Rightarrow \sec ^2 y \frac{d y}{d x}=\frac{d t}{d x} \) \( \frac{d t}{d x}+2 x t=x^3, \text { If }=e^{\int 2 x d x}=e^{x^2} \)…
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