Given equation

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

$(a)(10pts)$ Find general solutions.

$(b)(2pts)$ Give the largest interval where solution exists.

$(c)(2pts)$ Find transient term $if$ there $is$ any. $(b)(10pts)$

$\frac{dy}{dx}=y(x{y}^3-1)$

$y(0)=1$ Solve initial value problems

$(a)(10pts)$

$(sin(x+y^2)+e^{3x}-7)dx+(2ysin(x+y^2)+y-1)dy=0$

$y(0)=0(b)(12pts)$

$\frac{dy}{dx}=\frac{x+2y}{2x+y}$Find general solutions $of$ the given differential equations.

$(a)(10pts)$

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