0007.tex

\begin{exerciseStatement}


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


\begin{enumerate}[(a)]
\item \[ {x''} + {x'} = 6 \, {x} \hspace{2em}
           {x} (0)= 9 ,
           {x} '(0)= -2 \]
\item \[ 36 \, {y} = -{y''} \hspace{2em}
           {y} (0)= 0 ,
           {y} '(0)= 18 \]
\end{enumerate}
    
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {x} = 5 \, e^{\left(2 \, t\right)} + 4 \, e^{\left(-3 \, t\right)} \]\[ {y} = 3 \, \sin\left(6 \, t\right) \]
\end{exerciseAnswer}