Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I would like to solve the following differential equation

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

How should I proceed ?

share|improve this question
    
It's fairly well known that $\int e^{-x^2}$ can't be expressed in terms of elementary functions. –  Robert Mastragostino Jun 7 '12 at 17:33
1  
    
$y$ is the unknown function. I did not write $e^{-x^2}$. Edit : My bad I wrote ODE, which was confusing. I edited the post. –  vanna Jun 7 '12 at 17:37
1  
Just note that $dx/dy = \alpha^{-1}e^{y^2}$. –  sos440 Jun 7 '12 at 17:44
    
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 ? –  vanna Jun 7 '12 at 18:05

1 Answer 1

up vote 1 down vote accepted

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

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

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.