0009.tex

\begin{exerciseStatement}


 Use Euler's method with \(h= 0.10 \) to approximate \(x( 1.2 )\) and \(y( 1.2 )\) given the following system of IVPs. 

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

\begin{itemize}
\item \(x( 1.1 )\approx  -0.700 \) and \(y( 1.1 )\approx  -0.100 \)
\item \(x( 1.2 )\approx  -0.502 \) and \(y( 1.2 )\approx  -0.216 \)
\end{itemize}
    
\end{exerciseAnswer}