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Laplace transform and differential equations.

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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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Solution Summary

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

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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 ...

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