Solve the initial value problem y′+y=f(t),y(0)=0 where f(t)={1,−1, if t<4 if t≥4 Use h(t−a) for the Heaviside function shifte
d a units horizontally.
1 answer:
Looks like the function on the right hand side is

We can write it in terms of the Heaviside function,

as

Now for the ODE: take the Laplace transform of both sides:


Solve for <em>Y</em>(<em>s</em>), then take the inverse transform to solve for <em>y</em>(<em>t</em>):






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