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## Systems recordings

Here is a recoding of a solution to a system of linear, first-order differential equations with a slope field and solution curves near eigenvectors. or get it on You Tube, http://youtu.be/A-RwYm2SLiA Here is a recording of a similar system but with complex eigenvalues: http://youtu.be/q9nCdpdlqE4

## Exam 3

Here is the third test.  I have one more comprehensive part to post: coming soon. For now enjoy part 1 of the last test: mth256_exam3_summer12

## Fun with Trigonometry

The homogeneous solution is

Using variation of parameters we get a nonhomogeneous solution of

Distributing and regrouping

Reversing the cosine angle difference formula

Using the initial conditions $x(0)=0$, $\dot{x}(0)=0$, we get $c_1=\frac{-25}{18}$ and $c_2=0$ So a specific solution is

Regrouping and applying a difference to product formula

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