Ordinary Differential Equations

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The best source of knowledge for ODEs: video lectures from MIT.

http://ocw.mit.edu/OcwWeb/Mathematics/18-03Spring2004/VideoLectures/index.htm

I recommend this book: Differential Equations Problem Solvers

First order, linear, homogeneous equations

1.1 solution Solve the system of ODE's:

1.2 solution Solve

1.3 solution Solve

Second order, linear, homogeneous equations

2.1. solution

2.2. solution

2.3. solution

2.4. solution

Second order, linear, nonhomogeneous equations

4.1 solution

4.2 solution

4.3 solution Find a particular solution of


4.4 solution A ball is thrown straight up from the ground. How high will it go?

Nonlinear

5.1 solution

5.2 solution

5.3 solution


Laplace Transforms

The best introduction to the Laplace transform is from an undergrad MIT ODE class, starting at lecture 19 at the link above.

Here are some rules and transforms: http://en.wikipedia.org/wiki/Laplace_transform

6.1 solution

6.2 solution Find the Laplace transform of

6.3 solution Find the Laplace transform of


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