List of top Mathematics Questions on Differential Equations asked in AP PGECET

A function $y(x)$ such that $y(0) = 1$ and $y(1) = 4e$ is a solution of the differential equation $\frac{d^2y}{dx^2} - 2\frac{dy}{dx} + y = 0$. Then, $y(2)$ is equal to _______}

If $y(x) = C_1 \cos 2x + C_2 \sin 2x + A(x) \log (\sec 2x + \tan 2x)$ is the general solution of the differential equation $\frac{d^2y}{dx^2} + 4y = \tan 2x$, then $A(x) = \_\_\_\_\_\_\_$}