<exercise masterit-seed="2652" 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'= t^{2} x^{2} + 4 \, t^{2} y^{2} + 1 \hspace{2em}
x( -1 )= 0 </me><me>
y'= 2 \, x y^{2} + 4 \, t y - 3 \hspace{2em}
y( -1 )= -1 </me></statement><answer><ul><li><m>x( -0.90 )\approx 0.500 </m> and
<m>y( -0.90 )\approx -0.900 </m></li><li><m>x( -0.80 )\approx 0.883 </m> and
<m>y( -0.80 )\approx -0.795 </m></li></ul></answer></exercise>
