%Homogeneous ODEs with Constant Coefficients
%Math340

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{\Large
Homogeneous ODEs with Constant Coefficients
\footnote{Copyright \copyright 2002 Steve Chapin and Larry Snyder.
All rights reserved. Please address comments to young@math.ohiou.edu.}}
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Try the following in \textsc{MatLab}:\\
   \verb&   syms m&   \\
   \verb&   eqn1 = 'm^2 - 3*m-1 = 0'&  \\
   \verb&   eqn2 = 'm^4 - 4*m^3 + 14*m^2 - 20*m + 25 = 0'&  \\
   \verb&   solve(eqn1)&  \\
   \verb&   solve(eqn2)&

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For each of the following differential equations:

\begin{itemize}
    \item  Write down the auxiliary equation.

    \item  Write down, in standard mathematical notation, all of the 
           solutions to the auxiliary equation.
           (Use \textsc{MatLab} to find the solutions.)

    \item  Write down the general solution of the differential equation.
\end{itemize}

\bigskip

(a) \qquad $y''' + y'' - 6y' - 18y = 0$

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(b) \qquad $y^{(4)} - 2y''' - 6y'' + 16y' - 8y = 0$

\bigskip

(c) \qquad $y^{(4)} - 3y''' + 7y'' + 21y' - 26y = 0$

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(d) \qquad $y^{(5)} - 2y^{(4)} + 2y''' - 4y'' + y' - 2y = 0$

\bigskip

(e) \qquad $2y^{(5)} - y^{(4)} - 4y''' + 3y'' - 8y' - 12y = 0$

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