0006.tex

\begin{exerciseStatement}


 Use Euler's method with \(h= 0.10 \) to approximate \(x( -0.80 )\) and \(y( -0.80 )\) given the following system of IVPs. 

\[
        x'= -2 \, t^{2} x - 2 \, t^{2} y - 2 \hspace{2em}
        x( -1 )= 2 \]\[
        y'= -t^{2} x^{2} - x y^{2} \hspace{2em}
        y( -1 )= 0 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 

\begin{itemize}
\item \(x( -0.90 )\approx  1.40 \) and \(y( -0.90 )\approx  -0.400 \)
\item \(x( -0.80 )\approx  1.04 \) and \(y( -0.80 )\approx  -0.581 \)
\end{itemize}
    
\end{exerciseAnswer}