Given the differential equation:

$y^{\text{'}}=\frac{2x{y}^2+4x}{x^{2}y+y}$

$($a$)$ Identify the equation $($i$.$e$.,$ linear, separable, Bernoulli, homogeneous$).$

$($b$)$ Find the general solution.

$($c$)$ Find the solution satisfying $y(1)=0.$