# Diff eq - LT Discontinuous Sources HW

## Homework Statement ## Homework Equations ## 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

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Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement ## Homework Equations ## 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
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
$$\frac{1}{(s-a)(s-b)} = \frac{1}{a-b} \left[ \frac{1}{s-a} - \frac{1}{s-b} \right] \: \text{if} \; a \neq b$$

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
$$\frac{1}{(s-a)(s-b)} = \frac{1}{a-b} \left[ \frac{1}{s-a} - \frac{1}{s-b} \right] \: \text{if} \; a \neq b$$
That was so much help
5u(t−9)y1(t−9
I used this and worked like miracles for few questions, I was just confused of changing to and from the t-c.

Ray Vickson
Homework Helper
Dearly Missed
That was so much help

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I am glad. It does not always work, but when it does it makes life a lot easier.
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I used this and worked like miracles for few questions, I was just confused of changing to and from the t-c.