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Homework Statement
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 = ?
Homework Equations
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.