Question

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Answer 1

If you just need to check it: https://www.wolframalpha.com/input/?i=solve+y%27%27+%2B+3+y%27+%2B+2y+%3D+6+*+e^%28-t%29%2C+y%280%29+%3D+1%2C+y%27%280%29+%3D+2

Answer 2

\[\large \color{green}{y''}+3\color{royalblue}{y'}+2y=6e^{-t}\]
Hmm so we start by taking the Laplace of both sides right?
I'll be denoting \(\large \mathscr{L}\left[y\right]\) with \(\large Y\). Less writing :p heh.

So if we take the transform we get,
Umm sec I can't remember the transform of derivatives, i gotta look it up..

\[\large \color{green}{s^2Y-sy(0)-y'(0)}+3\color{royalblue}{\left[sY-y(0)\right]}+2Y=\frac{6}{s+1}\]

So this is what I have for my Transform so far, does this look correct so far? :O

Answer 3

And then I got the same answer as what @malevolence19 gave me just in a different form \[y(t)= (6t-2)e^{-t} + 3e^{-2t}\]

Answer 4

Oh cool c: Pshhh you don't need help then, looks like you did it just fine.

Answer 5

I wasn't sure! I second guess myself lol.