$($B$)$ Solve the following initial value problems $($IVP$)$ with separable equations:

$y-x{y}^{\text{'}}=3-2x^2{y}^{\text{'}},y(1)=-3.,y=\frac{3x}{1-2x}.$

$y^{\text{'}}(1-x^2)+xy=2x,y(2)=4.,y=\sqrt[\phantom{2}]{\frac{3}{4}(x^2-1)}+2.$

$e^{x+y}dy-dx=0,y(0)=-1.,y=ln(e^{-1}+1-e^{-x}).$

$y^{\text{'}}=y^{3}sinx,y(0)=-2.,y=\frac{-1}{\sqrt[\phantom{2}]{2cosx-\frac{7}{4}}}.$