Unformatted text preview: as our eigenvector v = ± 12 i 1 ² = ± 1 1 ² + i ±2 ² . Since complex eigenvalueeigenvectors come in conjugate pairs, we have the eigenvalues3 ± 2 i with corresponding eigenvectors ± 1 1 ² ± i ±2 ² We now have enough information to write down the general solution to the diﬀerential equation: x ( t ) = c 1 e3 t ³ ± 1 1 ² cos 2 t±2 ² sin 2 t ! + c 2 e3 t ´ ± 1 1 ² sin 2 t + ±2 ² cos 2 t µ 1...
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 Spring '07
 lee
 general solution, complex conjugate eigenvalues

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