Differential Equations Workbook For Dummies®

Chapter 10. Using Laplace Transforms to Solve Differential Equations

In This Chapter

• Figuring out Laplace transforms by hand or by referencing a table

• Applying Laplace transforms when derivatives are in play

• Solving differential equations with the help of Laplace transforms

Laplace transforms, a type of integral transform, are another good tool in your differential equation solving toolkit. They have the great charm of being able to turn differential equations into algebra problems. Using algebra, you then group terms and see whether you have the recognizable Laplace transform of anything. If you do, you can get the reverse Laplace transform and your answer all in one fell swoop.

Care to see a Laplace transform in action? Take a standard differential equation like this one:

y″ + 5y′ + 6y = 0

and find the Laplace transform of it, which looks like this (note that the {y} term always indicates a Laplace transform):

From there you need to consult tables of Laplace transforms. If you can identify the Laplace transform of what you have, you're in business!

In this chapter, you practice finding Laplace transforms and then solving equations by using them.