Let y = y(x) be the solution of the differential equation xdy = (y + x3 cosx)dx with y($\pi$) = 0, then $y\left( {{\pi \over 2}} \right)$ is equal to :

Question

Let y = y(x) be the solution of the differential

equation xdy = (y + x³ cosx)dx with y($\pi$) = 0, then $y\left( {{\pi \over 2}} \right)$ is equal to :

${{{\pi ^2}} \over 4} + {\pi \over 2}$

${{{\pi ^2}} \over 2} + {\pi \over 4}$

${{{\pi ^2}} \over 2} - {\pi \over 4}$

${{{\pi ^4}} \over 4} - {\pi \over 2}$

Solution

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