# [SOLVED]307.28.1 Find the general solution to the system of differential equations

#### karush

##### Well-known member
$\tiny{28.1}$
Find the general solution to the system of differential equations
\begin{align*}\displaystyle
y'_1&=y_1+5y_2\\
y'_2&=-2y_1+-y_2
\end{align*}
why is there a $+-y_2$ in the given
ok going to take this a step at a time... so..

$A=\left[\begin{array}{c}1 & 5 \\ -2 & -1 \end{array}\right]$
then
$\left[\begin{array}{c}1-\lambda & 5 \\ -2 & -1-\lambda \end{array}\right] =\lambda^2+9$ ????

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#### HallsofIvy

##### Well-known member
MHB Math Helper
yes, $$\displaystyle \left|\begin{array}{cc}1- \lambda & 5 \\ -2 & -1- \lambda\end{array}\right|= (1- \lambda)(-1- \lambda)+ 10= -1- \lambda+ \lambda+ \lambda^2+ 10= \lambda^2+ 9= 0$$.

Now, what are the values of $$\displaystyle \lambda$$?

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