Question

Solve the following system of equations using Laplace transforms, dx/dt - y = e^t, dy/dt + x = sint given that x = 1, y = 0 at t = 0.

Answer 1

We have x′(t) – y (t) = e^t ...(1) 

x(t) + y′(t) = sin t ...(2) 

where we have x (0) = 1, y (0) = 0 

Taking Laplace transforms on both sides of Eqns. (1) and (2)