0010.tex

\begin{exerciseStatement}


 Use Euler's method with \(h= 0.10 \) to approximate \(x( -1.8 )\) and \(y( -1.8 )\) given the following system of IVPs. 

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

\begin{itemize}
\item \(x( -1.9 )\approx  2.90 \) and \(y( -1.9 )\approx  -1.70 \)
\item \(x( -1.8 )\approx  6.09 \) and \(y( -1.8 )\approx  -3.84 \)
\end{itemize}
    
\end{exerciseAnswer}