Question about the General form to normal form of Diff Eq

Saladsamurai
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Homework Statement


The diff eq x(y&#039;)^2-4y&#039;-12x^3=0[/tex] takes the general form. Determine if the equation can be put in the normal form dy/dx=f(x,y)<br /> <br /> Well I have tried algebraically to isolate y&#039; and find that I cannot. So my question is, I have decided the answer is no. Now how do I explain why y&#039; cannot be isolated? Maybe this question is stupid...
 
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Isolating y' is just solving a quadratic equation. But they have two roots. Does that mean it's not a normal form? That's for you to answer. I don't know.
 

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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