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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 (Text):

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]

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# Mathematica Not Solving

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