# Laplace transform and differential equations.

Find the inverse Laplace transform of (s^3+s^2+2/s) / [s^2(s^2+3s+2)]

Using this (or otherwise), Find the solution of the equation y"+3y'+2y = 1-t

Find the transform of the following functions:

f(t) = (1+t^2)[u(t-1)-u(t-2)] where u(t) is the unit step function.

f(t) = sin(t) for 0<t<Pi and f(t)=0 for Pi<t<2*Pi

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The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore you can choose the format that is suitable to you.

Let me suggest that you check out the following site:

http://www.sosmath.com/diffeq/laplace/basic/basic.html

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Homogeneous solution:

Particular ...

#### Solution Summary

The solution shows how (among other things) to utilize partial fractions and inverse transform to solve a non-homogeneous differential equation.