Solving an ODE: Step-by-Step Guide and Tips

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Homework Statement


(4x^3 p^2-2p)dx+(2x^4 p-x)dp=0

The Attempt at a Solution


I have no idea how to solve it. It's not an exact differential and It's not of any famous ODE form that. Any ideas would be appreciated.
 
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Problem was solved. sorry that I opened a thread for it. I just needed to factor out (x^3p-1).
 
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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