0010.tex

\begin{exerciseStatement}


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


\begin{enumerate}[(a)]
\item \[ 6 \, {x'} - 8 \, {x} = {x''} \hspace{2em}
           {x} (0)= 3 ,
           {x} '(0)= 10 \]
\item \[ -64 \, {y} = {y''} \hspace{2em}
           {y} (0)= 2 ,
           {y} '(0)= -32 \]
\end{enumerate}
    
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {x} = 2 \, e^{\left(4 \, t\right)} + e^{\left(2 \, t\right)} \]\[ {y} = 2 \, \cos\left(8 \, t\right) - 4 \, \sin\left(8 \, t\right) \]
\end{exerciseAnswer}