Euler's differential equation explained

In mathematics, Euler's differential equation is a first-order non-linear ordinary differential equation, named after Leonhard Euler. It is given by:^[1]

(dy)/(dx) + (\sqrt{a _{0+a} _{1y} + a _{2} y ^{2} + a _{3} y ^{3} + a _{4} y ^{4})/() } = 0

This is a separable equation and the solution is given by the following integral equation:

\int (dy)/(\sqrt{a _{0+a} _{1} y + a _{2} y ^{2} + a _{3} y ^{3} + a _{4} y ^{4}) } + \int \frac = c

Notes and References

1. Ince, E. L. "L. 1944 Ordinary Differential Equations." 227.