0011.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. 

\[
        x'= 2 \, x^{2} y + 4 \, t x - 1 \hspace{2em}
        x( 0 )= 0 \]\[
        y'= -x^{2} y^{2} + 2 \, t y^{2} - 3 \hspace{2em}
        y( 0 )= 0 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 

\begin{itemize}
\item \(x( 0.10 )\approx  -0.100 \) and \(y( 0.10 )\approx  -0.300 \)
\item \(x( 0.20 )\approx  -0.205 \) and \(y( 0.20 )\approx  -0.598 \)
\end{itemize}
    
\end{exerciseAnswer}