Answer to Question #150976 in Differential Equations for Cypress

Question

If y(t)=c*e^(-2t)+t+1 is general solution to y'+p(t)*y=g(t), then p(t) and g(t)=?

Answer 1

Let $y(t)=Ce^{-2t}+t+1$ be the general solution of $y'+p(t)y=g(t)$.

Then $y'(t)=-2Ce^{-2t}+1$. Taking into account that $y'(t)+2y(t)=-2Ce^{-2t}+1+2(Ce^{-2t}+t+1)=2t+3$, we conclude that

$p(t)=2$ and $g(t)=2t+3.$