Laplace transform applied to differential equations
From Wikipedia, the free encyclopedia
The use of Laplace transform makes it much easier to solve linear differential equations with given initial conditions.
First consider the following relations:
Suppose we want to solve the given differential equation:
This equation is equivalent to
which is equivalent to
note that the f(k)(0) are initial conditions.
Then all we need to get f(t) is to apply the Laplace inverse transform to 
[edit] An example
We want to solve
with initial conditions f(0) = 0 and f ′(0)=0.
We note that
and we get
So this is equivalent to
We deduce
So we apply the Laplace inverse transform and get
[edit] Bibliography
- A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman & Hall/CRC Press, Boca Raton, 2002. ISBN 1-58488-299-9
