For $x \in \mathbb{R}$, let $y(x)$ be a solution of the differential equation

$\left(x^2-5\right) \frac{d y}{d x}-2 x y=-2 x\left(x^2-5\right)^2$ such that $y(2)=7$.

Then the maximum value of the function $y(x)$ is :

If $y(x)$ is the solution of the differential equation

$$ x d y-\left(y^{2}-4 y\right) d x=0 \text { for } x > 0, y(1)=2, $$

and the slope of the curve $y=y(x)$ is never zero, then the value of $10 y(\sqrt{2})$ is

Let f : R $$ \to $$ R be a differentiable function with f(0) = 0. If y = f(x) satisfies the differential equation $${{dy} \over {dx}} = (2 + 5y)(5y - 2)$$, then the value of $$\mathop {\lim }\limits_{n \to - \infty } f(x)$$ is ...........

Let $$y'\left( x \right) + y\left( x \right)g'\left( x \right) = g\left( x \right),g'\left( x \right),y\left( 0 \right) = 0,x \in R,$$ where $$f'(x)$$ denotes $${{df\left( x \right)} \over {dx}}$$ and $$g(x)$$ is a given non-constant differentiable function on $$R$$ with $$g(0)=g(2)=0.$$ Then the value of $$y(2)$$ is