JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) be a solution of the differential equation \((x \cos x) d y+(x y \sin x+y \cos x-1) d x=0\), \(0 < x < \frac{\pi}{2}\). If \(\frac{\pi}{3} y\left(\frac{\pi}{3}\right)=\sqrt{3}\), then \(\left|\frac{\pi}{6} y^{\prime \prime}\left(\frac{\pi}{6}\right)+2 y^{\prime}\left(\frac{\pi}{6}\right)\right|\) is equal to \(.........\).
- A \(4\)
- B \(6\)
- C \(8\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
\((x \cos x) d y+(x y \sin x+y \cos x-1) d x=0\), \(0 < x < \frac{\pi}{2}\) \(\frac{d y}{d x}+\left(\frac{x \sin x+\cos x}{x \cos x}\right) y=\frac{1}{x \cos x}\) \(I F=x \sec x\) \(y \cdot x \sec x=\int \frac{x \sec x}{x \cos x} d x=\tan x+c\)…
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