<exercise masterit-seed="7373" 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( 0.20 )</m> and <m>y( 0.20 )</m> given the following
system of IVPs.
</p><me>
x'= -2 \, t^{2} x^{2} - 2 \, t y^{2} + 3 \hspace{2em}
x( 0 )= -2 </me><me>
y'= -3 \, x^{2} y^{2} - 2 \, t^{2} x - 3 \hspace{2em}
y( 0 )= -2 </me></statement><answer><ul><li><m>x( 0.10 )\approx -1.70 </m> and
<m>y( 0.10 )\approx -7.10 </m></li><li><m>x( 0.20 )\approx -2.41 </m> and
<m>y( 0.20 )\approx -51.1 </m></li></ul></answer></exercise>
