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#### karush

##### Well-known member

- Jan 31, 2012

- 2,928

$\textrm{Solve the given equation by variation of parameters.}$

\begin{align*}\displaystyle

y''-10y'+25y&=2e^{5x}\\

\end{align*}

$\textrm{the homogeneous equation:}$

\begin{align*}\displaystyle

x^2-10x+25&=0\\

(x-5)^2&=0\\

x&=5\\

y_h&=c_1 e^{5x}+c_2x^{5x}

\end{align*}

$\textit{now what}$