What do you Know about ODE?

Calculus Level 4

\[\frac{dy}{dx}=-\dfrac{2e^{2x}\sin(y)+xy^2}{e^{2x}\cos(y)+x^2y}\] Given the ODE above and knowing the point \((0,\frac{\pi}{2})\) belongs to its solution. If the point \((\frac{\sqrt{a}}{\pi},\pi)\) belongs to the solution too, find the value of \(a\).

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