JEE Mains · Maths · STD 12 - 9. differential equations
If \(\cos \,x\,\frac{{dy}}{{dx}} - y\,\sin \,x = 6x,\,\left( {0 < x < \frac{\pi }{2}} \right)\) and \(y\left( {\frac{\pi }{3}} \right) = 0\), then \(y\left( {\frac{\pi }{6}} \right)\) is equal to
- A \( - \frac{{{\pi ^2}}}{{4\sqrt 3 }}\)
- B \( - \frac{{{\pi ^2}}}{2}\)
- C \( \frac{{{\pi ^2}}}{{2\sqrt 3 }}\)
- D \( - \frac{{{\pi ^2}}}{{2\sqrt 3 }}\)
Answer & Solution
Correct Answer
(D) \( - \frac{{{\pi ^2}}}{{2\sqrt 3 }}\)
Step-by-step Solution
Detailed explanation
\(\cos x \frac{d y}{d x}-y \sin x=6 x\) \(\Rightarrow \frac{d y}{d x}-y \tan x=6 x \sec x\) \(=\mathrm{e}^{-\int \tan x d x}=e^{-\log _{e} \sec x}=\frac{1}{\sec x}\) \(\therefore \) solution of equation…
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