Problem $1,15$pt

Solve the ODE $($a$),($b$),($c$)($d$),($e$)$ using Laplace transformation and partial fraction

expansion.

$($a$)y^{}(t)+y^{}(t)+3y(t)=0$;$y(0)=1,y^{}(0)=2$

$($b$)y^{}(t)-2y^{}(t)+4y(t)=0$;$y(0)=1,y^{}(0)=2$

$($c$)y^{}(t)+y^{}(t)=sint$;$y(0)=1,y^{}(0)=2$

$($d$)y^{}(t)+3y(t)=sint$;$y(0)=1,y^{}(0)=2$

$($e$)y^{}(t)+2y^{}(t)=e^t$;$y(0)=1,y^{}(0)=2$