Diff eq - LT Discontinuous Sources HW

[Arij]

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

 

[Ray Vickson]

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

 

[Arij]

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]

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.