Need help with a differential equation

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SUMMARY

The discussion focuses on solving the differential equation x² - 2px + y² - 2(y - p)y' = 0. The user expresses difficulty in finding an analytical solution and mentions using Mathematica for numerical simulations, but it fails to solve this specific equation. The user notes that the part without explicit x-dependence relates to the product log function, as indicated by WolframAlpha, but is uncertain how to incorporate the remaining terms.

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  • Understanding of differential equations, specifically first-order equations.
  • Familiarity with numerical simulation techniques.
  • Knowledge of Mathematica for computational solutions.
  • Basic understanding of the product log function and its applications.
NEXT STEPS
  • Research methods for solving first-order differential equations analytically.
  • Explore advanced features of Mathematica for handling complex equations.
  • Learn about the product log function and its implications in differential equations.
  • Investigate alternative software tools for solving differential equations, such as Maple or MATLAB.
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Mathematicians, physics students, and engineers dealing with differential equations, as well as anyone interested in numerical methods and analytical solutions in mathematical modeling.

Kvad
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Hi all,

I have derived a differential equation, which I don't know how to solve. I can do some numerical simulations, but would really be interested in, at least, knowing if an analytical solution exists, so would appreciate any help with it: (I have removed argument from y)

x2-2px+y2-2(y-p)y'y=0

Usually I just solve equations with mathematica, but it cannot tackle this one, though it doesn't look too bad...

Thanks!
 
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The part without explitic x-dependence leads to the product log function (WolframAlpha), I don't see an obvious way to take the other part into account.
 

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