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Let \(y = y(x)\) be the solution of the differential equation \(\mathrm{xdy}=\left(\mathrm{y}+{\mathrm{x}}^{3}\mathrm{co…

Q1

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