initial value problem?

1)Solve the initial value problem
(dy/dt)+2y=20sin(t)+20cos(t) with y(0)=1.

Please teach me how to make it looks like something dy= something dt

2)Find a continuous solution for this first order linear IVP with discontinuous RHS:
My answer are y(t)=e^(t^2)+2 0≤t≤2 & y(t)=3e^-(t^2) t>2

Thanks