Differential Equations question bank (Maths)

Which one of the following is the solution of the differential equation $x^2 \frac{d y}{d x}+9 x y=x^4(\text { for } x\gt0)$ given that $y=0$ when $x=1$ ?

Consider the differential equation
$\cos (y) \frac{d y}{d x}+\frac{1}{x} \sin (y)=x, \quad(x\gt0)$
given that $y=\frac{\pi}{2}$ at $x=\sqrt{3}$. Which one of the following is the value of $y$ at $x=\sqrt{\frac{3}{2}}$ ?