- #1

joshmccraney

Gold Member

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## Main Question or Discussion Point

Hi PF!

I am wondering if any of you can explain why Mathematica won't solve this ODE? I know an analytic solution exists (it's quadratic). Any help is greatly appreciated! $f0[x]$ is the name of the function.

I am wondering if any of you can explain why Mathematica won't solve this ODE? I know an analytic solution exists (it's quadratic). Any help is greatly appreciated! $f0[x]$ is the name of the function.

Code:

```
a = -1/5;
DSolve[{-((2 a f0[x])/(1 + a)) + x f0'[x] +
2 (f0'[x])^2 + f0[x] f0''[x] == 0,
f0[1] == 0, f0'[1] == -1/2}, f0[x], x]
```