I am trying to solve the following first order non-linear differential equation:
$$ \frac{\partial y}{\partial x} = -\sqrt{\frac{2(\sigma + 1)}{\sigma}} \sqrt{-\frac{1}{2y^{2}} + \frac{1}{8y^{8}}+\frac{3}{4}} $$
where, $\sigma$ is independent of both x and y. After, making use of separable equation, the above equation can be rewritten as: $$ \sqrt{\frac{8y^8}{6y^8 - 4y^6 + 1}} \partial y = \sqrt{2 \frac {\sigma + 1}{\sigma}} \partial x $$ Is there any trick that i can use to solve this problem for y ?