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I would like to solve the following differential equation

$$ y' = \alpha e^{-y^2} $$

How should I proceed ?

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    It's fairly well known that $\int e^{-x^2}$ can't be expressed in terms of elementary functions.2012-06-07
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    http://en.wikipedia.org/wiki/Examples_of_differential_equations#Separable_first-order_ordinary_differential_equations2012-06-07
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    $y$ is the unknown function. I did not write $e^{-x^2}$. Edit : My bad I wrote ODE, which was confusing. I edited the post.2012-06-07
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    Just note that $dx/dy = \alpha^{-1}e^{y^2}$.2012-06-07
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    You mean that I should find $y^{-1}$ and invert the result to get $y$ ? So as expected a non-closed formula... $y(x) = (\int_{y_0}^. \exp(u^2)du)^{-1}(x)$. Is that it ?2012-06-07
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    Use separation of variables, and then you have to find $\int e^{y^2}\,dy$, which can't be done using elementary functions.2012-06-08
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    To clarify, the ODE is separable.2012-06-08

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Solve the differential equation as x is a function in y. This gives the answer:

$$ x={\frac {1/2\,i\sqrt {\pi }\,{{\rm erf}\left(iy\right)}}{\alpha}} + C $$.