<exercise masterit-seed="6005" masterit-slug="F4" masterit-name="Implicit solutions for exact IVPs">
<statement>
<p>
Determine which of the following ODEs is exact.
</p>
<me> 5 \, y^{2} - t {y'} - y = -10 \, t y {y'} + 6 \, y^{2} {y'} </me>
<me> -6 \, t^{2} y {y'} + 6 \, t y - y = 6 \, y^{2} {y'} - 5 \, y^{2} </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> 5 \, y^{2} - t {y'} - y = -10 \, t y {y'} + 6 \, y^{2} {y'} </me>
<p>
Its implicit solution satisfying the initial value is:
</p>
<me> -5 \, t y^{2} + 2 \, y^{3} + t y = 6 </me>
</answer>
</exercise>
