ind the general solution $of$ the following differential equations:

$a.,xy\frac{dy}{dx}-(1+x)y^2=0$

$b.\frac{dy}{d}-ycot=y^{2}se{c}^2$

$c.x\frac{dy}{dx}-y=x^3+3x^2-2x$

$d.P\frac{dP}{dt}+P^{2}tant=P^{4}se{c}^{4}t$