Solve the following differential equations.

$($a$)xydx-(x^2+x^{2}y+y^3)dy=0$

$($b$)(ydx-xdy)+\sqrt[\phantom{2}]{xy}dy=0,x>0,y>0$

$($c$)\frac{dy}{dx}=\frac{2x-y+1}{x-2y+1},x-2y+10$