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#### karush

##### Well-known member

- Jan 31, 2012

- 2,886

Find a general solution to the system of differential equations

$\begin{array}{llrr}\displaystyle

\textit{given}

&y'_1=\ \ y_1+2y_2\\

&y'_2=3y_1+2y_2\\

\textit{solving }

&A=\begin{pmatrix}1 &2\\3 &2\end{pmatrix}\\

\textit{eigensystem}.

&\begin{pmatrix}1-\lambda &2\\3 &2-\lambda\end{pmatrix}

=\lambda^2-3\lambda -4 = (\lambda-4)(\lambda+1) = 0 \\

&\lambda = 4,-1

\end{array}$

so far,,, not sure what is next!