The Laplace transform method can be used to obtain the exact solution of ( ) and verify the results ( ), ( ), ( ), ( ) from Putzer's method. We outline how this is done for z(t) when λ 1 ̸ = λ 2 ; the remaining cases for x(t) and λ 1 = λ 2 are similar. The first step involves taking the Laplace transform of the inhomogeneous system (4). Letting x(t) ↔ X(s) and z(t) ↔ Z(s) be Laplace transform pairs we find