First-Order Linear ODE

First-order linear ODEs cover an enormous range of quantitative models — interest accrual, cooling bodies, exponential mixing, and (with the right forcing) the famous "two exponential clocks" problem from the green book.

Solve the initial value problem

$\frac{dy}{dt}+2y=e^{-t},y(0)=0.$

Give the explicit solution $y(t)$ and interpret what each term represents.