$(20$ points$)$ Find the solution to the initial value problem $($Hint: use superposition theorem$).$

a$).y^{\text{'}\text{'}}(x)-y^{\text{'}}(x)-2y(x)=cosx-sin2x$;

$y(0)=-\frac{7}{20},y^{\text{'}}(0)=\frac{1}{5}$

b$).$

$y^{\text{'}\text{'}}+2y^{\text{'}}+y=t^2+1-e^t$

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