III.1.8 Solution of linear ODEs using Laplace Transform

Following example illustrates the method of solving ODEs using Laplace Transform. Consider the following set of equations arisen from a modeling exercise:

	(III.27)
	(III.28)

With . Task is to find a solution for x(t) and y(t).

Taking Laplace Transform of eqns. (III.27) & (III.28) we obtain,

	(III.29)
	(III.30)

After rearrangement of the above we obtain,

	(III.31)
	(III.32)

Taking the inverse Laplace Transform we obtain,

	(III.33)
y(t)	(III.34)