"Laplace transform example" X = B / (s - i omega) Y = s - A B / (s - i omega) Cb = X / Y a = -i omega b = -A B check(Cb == B / (s^2 + a s + b)) k = sqrt(4 b - a^2) cb = B 2/k sin(1/2 k t) exp(-1/2 a t) ca = d(cb,t) / (B exp(i omega t)) ca cb -- verify solutions X = cos(1/2 k t) exp(-1/2 i omega t) + i omega / k sin(1/2 k t) exp(-1/2 i omega t) Y = 2 B / k sin(1/2 k t) exp(1/2 i omega t) check(ca == X) check(cb == Y) check(d(ca,t) == A exp(-i omega t) cb) check(d(cb,t) == B exp(i omega t) ca) check(eval(ca,t,0) == 1) check(eval(cb,t,0) == 0) "ok" Run