0001.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. 

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

\begin{itemize}
\item \(x( -0.90 )\approx  0.500 \) and \(y( -0.90 )\approx  -0.900 \)
\item \(x( -0.80 )\approx  0.883 \) and \(y( -0.80 )\approx  -0.795 \)
\end{itemize}
    
\end{exerciseAnswer}