$2-$ Solve the following differential equations:

a$)t{y}^{\text{'}}+y=t^2{y}^{2}sint,y(\frac{}{2})=1$

$(10$ points$)$

b$)y^{\text{'}\text{'}}+2y^{\text{'}}+2y=2t^2$

$y(0)=2,y^{\text{'}}(0)=1$

$(10$ points$)$

c$)y^{\text{'}\text{'}}+2y^{\text{'}}+y=2e^{-t}$

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

$(10$ points$)$