0008.tex

\begin{exerciseStatement}


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


\begin{enumerate}[(a)]
\item \[ 100 \, {x} = -{x''} \hspace{2em}
           {x} (0)= -2 ,
           {x} '(0)= -50 \]
\item \[ {y''} + 3 \, {y'} = 10 \, {y} \hspace{2em}
           {y} (0)= 7 ,
           {y} '(0)= -14 \]
\end{enumerate}
    
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {x} = -2 \, \cos\left(10 \, t\right) - 5 \, \sin\left(10 \, t\right) \]\[ {y} = 3 \, e^{\left(2 \, t\right)} + 4 \, e^{\left(-5 \, t\right)} \]
\end{exerciseAnswer}