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s11_mthsc208_ws4c-SystemsComplex

# s11_mthsc208_ws4c-SystemsComplex - MthSc 208(Spring 2011...

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MthSc 208 (Spring 2011) Worksheet 4c MthSc 208: Differential Equations (Spring 2011) In-class Worksheet 4c: Systems of differential equations (complex eigenvalues) NAME: Consider the system of differential equations: x 0 1 = - 0 . 5 x 1 + x 2 , x 1 (0) = 0 x 0 2 = - x 1 - 0 . 5 x 2 , x 2 (0) = 1 1. Write this in matrix form, x 0 = Ax + b . 2. Given that the eigenvalues of A are λ 1 = - 1 2 + i and λ 2 = - 1 2 - i , with associated eigenvectors v 1 = (1 , i ) and v 2 = (1 , - i ), write the general solution to x 0 = Ax . 3. Use Euler’s formula ( e it = cos t + i sin t ) to write a solution (e.g., x 1 ( t )) as a sum of its real and

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s11_mthsc208_ws4c-SystemsComplex - MthSc 208(Spring 2011...

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