# Analytic solution for high-order non-linear differential equation

Is there a way to analytically solve an equation of this form:

$$y''''[x]+y[x]*y'''[x]=0$$

where the initial conditions for y through the fourth derivatives are known.

I have used lower-order substitutions to convert the equation to a system of first-order differential equations, and now I am appeared forced to apply a numerical method e.g., Runge-Kutta. However, an analytical form would be much more appreciated.

Thanks!

• i think a numerical solution is a good choice – Dr. Sonnhard Graubner Mar 28 '18 at 15:52
• Thanks for the confirmation. I just wanted to make sure there wasn't some math magic I am missing to transform this equation :) – user3213998 Mar 28 '18 at 16:36