# Math Help - using the Laplace transform to solve...

1. ## using the Laplace transform to solve...

man these problems are long but here goes...

ok i am not sure what im doing wrong but my partial fraction that I am getting is not giving me the right answer...one i have 7 terms and the book has 4 terms in its answer.

$2y'''+3y''-3y'-2y=e^{-t}$ y(0)=0, y'(0)=0 , y''(0)=1

after making the substitutions i got:

$$-\frac{8}{9\,\left( 2\,s+1\right) }+\frac{2}{9\,\left( s+2\right) }+\frac{2}{s+1}+2\,{s}^{2}+s+\frac{2}{9\,\left( s-1\right) }-4]$$

i was hoping someone could tell me where i went wrong....

thanks

2. sorry here is the problem...

$2y'''+3y''-3y'-2y=e^{-t}$

3. Hmm. Here's what I get:

You can use the Heaviside cover-up method to get the constants, and then fire away with the inverse. As you can see, there are only 4 terms.

Does that help?

4. ok i didnt get the 2s+3 let me go back and add that and finish working out the problem. thanks!

5. You're welcome, as always.