# Diff eq - LT Discontinuous Sources HW

1. Aug 8, 2016

### Arij

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
this is my attempt, I figured this would be easier than typing.

any how, I find partial fraction method is so time consuming and very algebraically complicated, is there a trick or another method I could use to make this easier?

thanks

2. Aug 8, 2016

### Ray Vickson

Convert $Y_1(s) = \frac{1}{(s+3)(s-4)(s-8)}$ to partial fractions, then multiply by $5 e^{-9s}$ later; better still, find the inverse of $Y_1(s)$ as $y_1(t)$; the solution is then $5 u(t-9)y_1(t-9)$.

The partial fractions can be found easily (but still with some algebra) by applying successively the identities
$$\frac{1}{(s-a)(s-b)} = \frac{1}{a-b} \left[ \frac{1}{s-a} - \frac{1}{s-b} \right] \: \text{if} \; a \neq b$$

3. Aug 10, 2016

### Arij

That was so much help
I used this and worked like miracles for few questions, I was just confused of changing to and from the t-c.

4. Aug 10, 2016