Non-linear differential equation

Heimisson
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Hi I'm writing a function (matlab) in my numerical analysis class that descripes in a certain way a non-linear differential equations with Robin BC that I will then feed to a program that uses finite difference method to solve it. It seems to work but I wanted to look for a site or program that could solve some example equations numerically so I can be sure that it's working correctly. WolframAlpha doesn't seem to handle Robin BC and by googling I only found programs that don't work on mac.

thanks
 
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Never mind I found a solution to the equation, although a trustworthy program would be useful.
 
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...
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