<exercise masterit-seed="6130" masterit-slug="N2" masterit-name="Euler's method for approximating IVP solutions"><statement><p>
Use Euler's method with <m>h= 0.10 </m> to approximate
<m>x( -0.80 )</m> and <m>y( -0.80 )</m> given the following
system of IVPs.
</p><me>
x'= -2 \, t^{2} x - 2 \, t^{2} y - 2 \hspace{2em}
x( -1 )= 2 </me><me>
y'= -t^{2} x^{2} - x y^{2} \hspace{2em}
y( -1 )= 0 </me></statement><answer><ul><li><m>x( -0.90 )\approx 1.40 </m> and
<m>y( -0.90 )\approx -0.400 </m></li><li><m>x( -0.80 )\approx 1.04 </m> and
<m>y( -0.80 )\approx -0.581 </m></li></ul></answer></exercise>
