# Differential Equation - Inverse Laplace Transformation

## Homework Statement

Find the inverse laplace transformation of $$\frac{2s^2 +3s - 2}{s(s+1)(s-2)}$$

## The Attempt at a Solution

$$L^{-1} \frac{2s^2 +3s - 2}{s(s+1)(s-2)} = L^{-1}\frac{1}{2} + L^{-1}\frac{1}{s+1} +2 L^{-1}\frac{1}{s-2} = 1 - e^{-t} + 2e^{2t}$$

Have I made a mistake somewhere?

and does anyone know where I can find a web site practice problems (preferably with answers so I can check) similiar to this one?

gabbagabbahey
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## Homework Statement

Find the inverse laplace transformation of $$\frac{2s^2 +3s - 2}{s(s+1)(s-2)}$$

## The Attempt at a Solution

$$L^{-1} \frac{2s^2 +3s - 2}{s(s+1)(s-2)} = L^{-1}\frac{1}{2} + L^{-1}\frac{1}{s+1} +2 L^{-1}\frac{1}{s-2} = 1 - e^{-t} + 2e^{2t}$$

Have I made a mistake somewhere?

and does anyone know where I can find a web site practice problems (preferably with answers so I can check) similiar to this one?

Assuming that the $\mathcal{L}^{-1}[\frac{1}{2}]$ was just a typo, and you meant to write $\mathcal{L}^{-1}[\frac{1}{s}]$, then yes, you are correct.

As for practice problems and solutions, a quick Google search came up with http://ece.olin.edu/dynamics/handouts/ogata_ch2_examples_practice.pdf [Broken]. I haven't checked the contents for correctness, but there are several worked problems in there (and I'm sure you can find more yopurself with Google!).

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Yea, I meant to write 1/s.