Solutions to linear differential equations can be written using convolutions as y(t) =y_h(t) + (h(t) * g(t)| |y_h| is the solution to the associated homogeneous differential equation with the given initial values (RHS is 0, use given ICs). |h(t|) is the impulse response (ignore the initial values and forcing function). g(t)| is the forcing function (ignore the initial values and differential equation). Use the form above to write the solution to the differential equation y" + 2y' -3y = 6t^2 e^-3t with y(0) = 12, y'(0) =4| y =| +(| *|)|
