Find the function satisfying the differential equation y' - 2y = -9e^ {-1t} and y(0) = -3?

Answer 1

Your solution is y(t) = -6e^2t + 3e^-t

^{Using Laplace Transforms, the equation becomes Y(s) = -6/(s-2) + 3/(s+1) after using the fact that y(0) = -3}

^{The inverse transform yields the solution above.}