# Derivative Formulas; Using the Laplace Transform to Solve Linear ODEs

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Lesson Summary:

In this lesson, you will learn how to use the Laplace transform to solve linear differential equations with constant coefficients. The Laplace transform requires a growth condition on a function to exist, called exponential type. The Laplace transform also requires initial value problems to be solved, where the initial conditions must be given as unknown numbers. By taking the Laplace transform of the differential equation and initial conditions, you can solve for the original function that satisfies the equation and the initial conditions.

Lesson Description:

Derivative Formulas; Using the Laplace Transform to Solve Linear ODEs -- Lecture 20. Learn how to use the Laplace Transform to solve problems.

Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 27, 2008). License: Creative Commons BY-NC-SA.

• What is the Laplace Transform?
• How do you use the Laplace Transform to solve differential equations?
• How do you know the Laplace Transform will exist?
• How do you know if a function is of exponential type?
• #### Staff Review

• Currently 4.0/5 Stars.
This lecture shows how the Laplace Transform is actually used to solve linear differential equations. You will learn when you can use the transform and how to use it. Some actual problems are done and the Laplace Transform is used to solve them. A truly useful lecture.
• #### Aishah

• Currently 3.0/5 Stars.
Its okay!!!!!!!!