Laplace Transform: Can someone please help me understand how to arrive at the attached solution to this problem? I'm not understanding what we are doing to make "adjustments" to the numerators...my answers continue to be off by constants. http://i42.tinypic.com/67l6s3.jpg

Question

Laplace Transform:  Can someone please help me understand how to arrive at the attached solution to this problem? I'm not understanding what we are doing to make "adjustments" to the numerators...my answers continue to be off by constants.  http://i42.tinypic.com/67l6s3.jpg

anonymous · Answer

I came up with 3s/(s^2 + 4) + 3/(s+2)

anonymous · Answer

http://tutorial.math.lamar.edu/Classes/DE/DE.aspx

ash2326 · Answer

@Nisha318 did you get it?

turingtest · Answer

The relevant transforms here are$$\mathcal L\{y'(t)\}=sY(s)-y(0)$$and$$\mathcal L\{\cos (at)\}={s\over a^2+s^2}$$

turingtest · Answer

I think you just made an algebra mistake @Nisha318 
on the when you divided both sides by s+2 you forgot to put that factor under the 3s part...

turingtest · Answer

in the part when*

anonymous · Answer

I already printed out and read Paul's Notes from this section....still didn't understand why I didn't come up with the solution.

anonymous · Answer

oh yes, I forgot to put s + 2 under the 3s ...thanks

turingtest · Answer

welcome :)

anonymous · Answer

I think I'll need partial fract decomp to simplify that 3s/ (s^2 + 4) (s+2) part....I'll try it out.

turingtest · Answer

yeah, I haven't tried it yet, but I assumed you would use PF
let me know if you get stuck