Hello, I am having great difficulty with the following problem:
where for and for . Initial values are and .
I wrote as and used Laplace transforms to get
.
Originally I distributed the , solved for and ended up with some crazy partial fractions, but I think this definitely can't be right as I'm supposed to end up with another piecewise function as my answer. Could anyone point me in the right direction? I have never done a piecewise function with functions of t as the values.
Okay, I get the solutions
for the first one and
for the second.
These are similar in form to the solution I got in my original attempt at the problem, though I had crazy coefficients. I just don't understand what to do next as I think we're supposed to end up with a function of the form
and then rewrite it in piecewise form.