We are working on finding the particular solution for the first-order linear constant-coefficient ordinary differential equation:

Question

RCdvP(t)dt+vP(t)=Vicos⁡(ωt)
The new idea is to find the particular solution for the related equation

RCdvPS(t)dt+vPS(t)=Viest
because we expect that this solution is easy to get and it will help to find the particular solution for the original equation.

If you try vPS(t)=Vpest you will find that it will work; you can solve for Vp. In the space provided below write an algebraic expression for Vp in terms of Vi, s, R and C.