- #1

karush

Gold Member

MHB

- 3,269

- 5

Solve IVP

$\begin{array}{rl}x' & = 2x + 2y\\y' & = -4x + 6y\\x(0) & = 2\\y(0) & = -3

\end{array}$

assume we can proceed with this first

$A=\left[\begin{array}{rr}2&2\\-4&6\end{array}\right]\\

A-rI=\left[\begin{array}{rr}2-r&2\\-4&6-r\end{array}\right]=r^{2} -8r + 20 = 0 \quad r_1 = 4 -2 i \quad r_2=4+2i$

$\begin{array}{rl}x' & = 2x + 2y\\y' & = -4x + 6y\\x(0) & = 2\\y(0) & = -3

\end{array}$

assume we can proceed with this first

$A=\left[\begin{array}{rr}2&2\\-4&6\end{array}\right]\\

A-rI=\left[\begin{array}{rr}2-r&2\\-4&6-r\end{array}\right]=r^{2} -8r + 20 = 0 \quad r_1 = 4 -2 i \quad r_2=4+2i$

**eigenvector:**$\left[\begin{array}{c}\dfrac{1}{2} + \dfrac{i}{2}\\1\end{array}\right]$**eigenvector: $\left[\begin{array}{c}\dfrac{1}{2} - \dfrac{i}{2}\\1\end{array}\right]$**

so farso far

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