Laplace Transform can be used for solving differential equations by converting the differential equation to an algebraic equation and is particularly suited for differential equations with initial conditions.

The solution requires the use of the Laplace of the derivative:-

Consider the first order differential equation for y(t) below:-

For a unit step V(S) is shown below

For a unit ramp, the Laplace transform V(s) is

For second order equations:-

y''(t) + by'(t) + cy(t) = V(t)

Laplace transform gives s

and Y(s) = V(s)/(s

Instead of writing out the expressions, the result is summarised in the following applet which shows solutions of first and second order equations with step, ramp and sine inputs. It also shows the solution of a third order equation with step and sine inputs.

Scrollbar 0 changes the function of the applet and can be changed from 0 to 7 to show 1st, 2nd and 3rd order solutions.

In each case the contribution from the initial conditions are also shown.

Copyright 1996 © Cuthbert A. Nyack.