points$).$ Consider the following differential equation.

$x\frac{dy}{dx}+y=x^2{y}^2$

$($a$)$ Write the ODE as a Bernoulli's Equation $(d\frac{y}{d}x+P(x)y=Q(x)y^n.)$

$($b$)$ Convert it into a Linear Equation by an appropriate substitution.

$($c$)$ Solve the Linear Equation obtained in the above part$($b$).$

$($d$)$ Write down the explicit solution.