# How do we solve the following differential equation? ( y <mrow class="MJX-TeXAtom-ORD">

How do we solve the following differential equation?
$\left(y{}^{\prime }{\right)}^{2}+p\left(x\right)\left(1+{y}^{2}{\right)}^{3}=0$
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Hayley Mccarthy
Here is one approach.
Given:
$\left({y}^{\prime }{\right)}^{2}+p\left(x\right)\left({y}^{2}+1{\right)}^{3}=0$
We can solve for y' by taking square roots, yielding:

We can now separate and integrate: