Solving a piecewise function by Laplace transform

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.

Re: Solving a piecewise function by Laplace transform

Quote:

Originally Posted by

**Ragnarok** 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.

It might help you to try to solve the two following DEs...

and .

Re: Solving a piecewise function by Laplace transform

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.

Re: Solving a piecewise function by Laplace transform

I just solved this problem with the help of my teacher. Thanks!