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Let \(y=y(x)\) be the solution of the differential equation \(xdy=\left(y+{x}^{3}\cos x\right)dx\) with \(y(\pi )=0\), t…

Q1

Let \(y=y(x)\) be the solution of the differential equation \(xdy=\left(y+{x}^{3}\cos x\right)dx\) with \(y(\pi )=0\), then \(y\left(\frac{\pi }{2}\right)\) is equal to :

[JEE Main 2021, 25 Jul (Shift 2)]

a

\(\frac{{\pi }^{2}}{4}-\frac{\pi }{2}\)

b

\(\frac{{\pi }^{2}}{4}+\frac{\pi }{2}\)

c

\(\frac{{\pi }^{2}}{2}-\frac{\pi }{4}\)

d

\(\frac{{\pi }^{2}}{2}+\frac{\pi }{4}\)

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