1. The problem statement, all variables and given/known data Solve the IVP : dy/dt + y = f(t) y(0) = -5 where f(t) = -1, 0 <= t < 7 -5, t >= 7 y(t) for 0 <= t < 7 = ? y(t) for t >= 7 = ? 2. Relevant equations 3. The attempt at a solution So I have never seen a problem of this type, excuse my silly mistakes if I'm interpreting this question wrong. At first glance, I assume what the question is asking for is for me to solve what looks like two linear first order equations with the Laplace transform. I start at the first value of f(t), substitute -1 in where f(t) is, and then take the Laplace transform. Giving me: L(y' + y = -1), which is s * L(S) - y(0) + 1/s^2 = -1/s I then isolate for L(S), and take the inverse Laplace. Before I go any further, could anyone tell me if I'm coming at this problem correctly? I don't think it's right, since by my logic, I could solve this as if it was a first order linear and get the same result when I use Laplace, but they don't equal. Thanks for any assistance.