Differential Equations · JEE Advanced previous year questions

Let $y(x)$ be the solution of the differential equation $$x^2\frac{dy}{dx}+xy=x^2+y^2,x>\frac{1}{e},$$ satisfying $y(1)=0$. Then the value of $2\frac{(y(e){)}^2}{y(e^2)}$ is ____.

For $x\in \mathbb{R}$, let $y(x)$ be a solution of the differential equation $$(x^2-5)\frac{dy}{dx}-2xy=-2x(x^2-5{)}^2\text{ such that }y(2)=7.$$ Then the maximum value of the function $y(x)$ is ____.