# Laplace Transforms, Solution of Differential Equations,

(1) Use Laplace Transforms to solve Differential Equation

y'' - 8y' + 20 y = t (e^t) , given that y(0) = 0 , y'(0) = 0

(2) Use Laplace Transforms to solve Differential Equation

y''' + 2y'' - y' - 2y = Sin 3t , given that y(0)=0 , y'(0)=0 ,y''(0)=0, y'''(0)=1

Note: To see the questions in their mathematical form please download the attached file.

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#### Solution Summary

The Differential Equations y'' - 8y' + 20 y = t (e^t), y''' + 2y'' - y' - 2y = Sin 3t , given that y(0)=0 , y'(0)=0 ,y''(0)=0, y'''(0)=1 are solved using Lapalace Transforms in the given attachment. The method of solving the equations is explained in a lucid manner such a way that the students can work out other similar problems independently using this method.

The solution is given in minute detail so that the students may not feel difficulty in understanding and applying the method to solve other problems of the same model.