0003.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. 

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

\begin{itemize}
\item \(x( 0.10 )\approx  0.100 \) and \(y( 0.10 )\approx  -2.30 \)
\item \(x( 0.20 )\approx  0.223 \) and \(y( 0.20 )\approx  -2.43 \)
\end{itemize}
    
\end{exerciseAnswer}