<exercise masterit-seed="8685" masterit-slug="F4" masterit-name="Implicit solutions for exact IVPs">
<statement>
<p>
Determine which of the following ODEs is exact.
</p>
<me> 0 = 20 \, y^{3} {y'} - 4 \, t^{2} {y'} - 8 \, t y - 10 \, t </me>
<me> 6 \, t^{2} y {y'} - 4 \, t y {y'} - y = -8 \, t y </me>
<p>
Then find an implicit solution for this exact ODE
satisfying the initial value
<m>y( 1 )= -1 </m>.
</p>
</statement>
<answer>
<p>The following ODE is exact.</p>
<me> 0 = 20 \, y^{3} {y'} - 4 \, t^{2} {y'} - 8 \, t y - 10 \, t </me>
<p>
Its implicit solution satisfying the initial value is:
</p>
<me> 5 \, y^{4} - 4 \, t^{2} y - 5 \, t^{2} = 4 </me>
</answer>
</exercise>
