References

1. will-squaring-both-sides-of-the-ode-change-its-type Thanks to this answer which gave the main hint on how to solve such ode. I expanded this idea for a more general cases and different exponents.
2. Wikipedia entry on D’Alembert’s equation This show alternative method to solve the ode for \(\frac {1}{2}\).
3. Wikipedia entry on Riccati equation
4. Wikipedia entry on Abel ode
5. paper: Exactness of Second Order Ordinary Differential Equations and Integrating Factors by R. AlAhmad, M. Al-Jararha and H. Almefleh