0001.tex

\begin{exerciseStatement}


Explain how to find the particular solution to each given IVP.


\begin{enumerate}[(a)]
\item \[ 36 \, {x} = -{x''} \hspace{2em}
           {x} (0)= 1 ,
           {x} '(0)= -12 \]
\item \[ 0 = 10 \, {y} + {y''} - 7 \, {y'} \hspace{2em}
           {y} (0)= -2 ,
           {y} '(0)= -13 \]
\end{enumerate}
    
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {x} = \cos\left(6 \, t\right) - 2 \, \sin\left(6 \, t\right) \]\[ {y} = -3 \, e^{\left(5 \, t\right)} + e^{\left(2 \, t\right)} \]
\end{exerciseAnswer}