Solving ODEs: Is There Any Hope?

[James4]

Hello

coming from Discrete Mathematics, I have very little knowledge in Solving ODEs:

I have the following equation (where E(x) is an ordinary generating function).

$E'(x) = \frac{(E(x)*E(x) +E(x)-x)}{2x*E(x)}$

with E(0) = 0
Is there any hope to solve this equation?

 

[mathwonk]

there is always hope. have you looked at picard's method? what do you mean by "solve"? the usual procedure is to give a sequence of approximations that converge to a solution.

 

[JJacquelin]

Hello !
The analytical solution involves the special function erfi.
The solution is expressed on a parametric form (see attachment).

The part previously entitled "Formal solution" has been deleted. There was a mistake in it.