0004.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. 

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

\begin{itemize}
\item \(x( -0.90 )\approx  -4.70 \) and \(y( -0.90 )\approx  2.10 \)
\item \(x( -0.80 )\approx  -11.8 \) and \(y( -0.80 )\approx  29.3 \)
\end{itemize}
    
\end{exerciseAnswer}