0006.tex

\begin{exerciseStatement}


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


\begin{enumerate}[(a)]
\item \[ -{x''} = 12 \, {x} + 7 \, {x'} \hspace{2em}
           {x} (0)= -3 ,
           {x} '(0)= 10 \]
\item \[ -{y''} = 16 \, {y} \hspace{2em}
           {y} (0)= -3 ,
           {y} '(0)= -4 \]
\end{enumerate}
    
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {x} = -2 \, e^{\left(-3 \, t\right)} - e^{\left(-4 \, t\right)} \]\[ {y} = -3 \, \cos\left(4 \, t\right) - \sin\left(4 \, t\right) \]
\end{exerciseAnswer}