Solve the following differential equations.

$($a$)2y^{\text{'}\text{'}}2y^{\text{'}}3y=0$

$($b$)y^{\text{'}\text{'}}-2y^{\text{'}}y=x^2{e}^x$

$($c$)y^{\text{'}\text{'}}2y^{\text{'}}y=0$ subject to $y(-1)=0,y^{\text{'}}(0)=0.$

$($d$)y^{\text{'}\text{'}}-y=\frac{2e^x}{e^x{e}^{-x}}$