Solving Differential Equations of Type R'' + R' +R[(constants) + e^(-R^2)] = 0

Nusc
Messages
752
Reaction score
2

Homework Statement

What method would you use to solve DE's of this type
R'' + R' +R[(constants) + e^(-R^2)] = 0

?

Homework Equations


The Attempt at a Solution

 
Physics news on Phys.org
That is a very badly non-linear differential equation. I suspect that a numerical (approximate) solution would be the best you could do.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top