In physics we're told often that there is no analytical way to solve most nonlinear differential equations (I don't know if this can be proven or not, or it's just assumed because no one has found a way to do it), so we use a computer to solve them numerically.(adsbygoogle = window.adsbygoogle || []).push({});

I'm wondering though, assuming itisimpossible to solve a differential equation by analytical means, does that mean that there is no analytical solution which exists? That is, could you somehow guess some well-defined function that satisfies the nonlinear equation, even if there's no way of directly solving the equation for it?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Solvability v.s. the existance of a solution for nonlinear ODE's

**Physics Forums | Science Articles, Homework Help, Discussion**