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 want to solve $$\frac{dy}{dx}=e^{x^{2}}.$$ i using variable separable method to solve this but after some stage i stuck with the integration of $\int e^{x^{2}}dx$. i dont know what is the integration of $\int e^{x^{2}} dx$. Please help me out!

share|improve this question
    
There is no closed form integral of $e^{x^2}$. Are you sure you don't have a typo? –  Arkamis Jul 20 '12 at 4:03
3  
@Ed: it has a closed form. It's not elementary, however. –  J. M. Jul 20 '12 at 4:10
1  
Why in this green earth was this question downvoted? –  J. M. Jul 20 '12 at 5:39
1  
@J.M. Maybe someone was on the blue part of Earth. –  Pedro Tamaroff Jul 20 '12 at 7:04
1  
@Rahul: I wrote a long-ish answer to that question many moons ago, but the gist is, I consider the error function as a "known quantity", and I thus treat it as a closed form. –  J. M. Jul 20 '12 at 7:43
show 3 more comments

1 Answer

up vote 3 down vote accepted

$$ \frac{dy}{dx}=e^{x^{2}} $$ has no elementary solution. The error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape which occurs in probability, statistics and partial differential equations. It is defined as: $$ \operatorname{erf}(x) = \frac{2}{\sqrt{\pi}}\int_{0}^x e^{-t^2} dt. $$ See the link for reference and more information and thus, J.M. ...?

share|improve this answer
3  
...and thus, the solution of the DE is $y=-\frac{i\sqrt\pi}{2}\mathrm{erf}(ix)+C$. (the imaginary error function) –  J. M. Jul 20 '12 at 5:41
add comment

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.