Thread: Laplace / Initial Value system

Q = solve initial value system using laplace

x’ + y’ + x – y = 0, x’ + 2y’ + x = 1
x(0) = y(0) = 0

any guidance would be great.

Originally Posted by john1985

Q = solve initial value system using laplace

x’ + y’ + x – y = 0, x’ + 2y’ + x = 1
x(0) = y(0) = 0

any guidance would be great.

Let LT[y(t)] = Y(s) and LT[x(t)] = X(s). Then the system becomes

(s - 1)Y + (s + 1)X = 0 .... (1)

2sY + (s + 1)X = 1 .... (2)

Solve for X = X(s) and Y = Y(s) and then take the inverse Laplace transform to get x = x(t) and y = y(t).