AJSesinando
Using Green's Formula and Convolution to Solve a Linear ODE with Rest Initial Conditions
Green's formula and convolution let you solve a linear differential equation that starts at rest, for any forcing function on the right side. You take the weight function (the solution when the forcing is an instantaneous impulse) and convolve it with the forcing function. A convolution of f and g is the integral from 0 to t of f(tau) times g(t minus tau) d tau.