0002.tex

\begin{exerciseStatement}


 Use Euler's method with \(h= 0.10 \) to approximate \(x( 0.20 )\) and \(y( 0.20 )\) given the following system of IVPs. 

\[
        x'= -2 \, t^{2} x^{2} - 2 \, t y^{2} + 3 \hspace{2em}
        x( 0 )= -2 \]\[
        y'= -3 \, x^{2} y^{2} - 2 \, t^{2} x - 3 \hspace{2em}
        y( 0 )= -2 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 

\begin{itemize}
\item \(x( 0.10 )\approx  -1.70 \) and \(y( 0.10 )\approx  -7.10 \)
\item \(x( 0.20 )\approx  -2.41 \) and \(y( 0.20 )\approx  -51.1 \)
\end{itemize}
    
\end{exerciseAnswer}