Solving a Nonlinear Differential Equation: y+4y^2=(y^(4)+x)y

Laura1321412
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Homework Statement


y+4y^2=(y^(4)+x)y', IC: y(1)=1


Homework Equations


?


The Attempt at a Solution



Ive tried to figure out a substitution that will make this linear, and i can't seem to figure one... I am unsure of how to approach this?
 
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It must be a mistake in your problem. The <Mathematica> softare running at www.wolframalpha.com returns a solution spreading on 4 pages full of horrible radicals.
 

Thread 'Finding the nth roots of a complex number'

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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