Differential Equations - Bernoulli Problem

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SUMMARY

The discussion focuses on solving the Bernoulli differential equation represented by y' = 2xy/(x^2 - y^2). The primary method suggested involves using the substitution u = y/x to facilitate separation of variables. Participants emphasize the importance of manipulating the equation by dividing the numerator and denominator by x^2 to achieve the desired form. This approach allows for the elimination of y and y' terms, streamlining the solution process.

PREREQUISITES
  • Understanding of Bernoulli differential equations
  • Familiarity with variable separation techniques
  • Knowledge of substitution methods in differential equations
  • Basic calculus concepts, including derivatives
NEXT STEPS
  • Study the method of solving Bernoulli equations in detail
  • Learn about variable separation in differential equations
  • Explore substitution techniques for simplifying complex equations
  • Practice solving differential equations using the u-substitution method
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Students studying differential equations, mathematics educators, and anyone looking to enhance their problem-solving skills in calculus and differential equations.

steelphantom
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Homework Statement



Solve the equation y' = \frac{2xy}{x^2-y^2}

Homework Equations



The Bernoulli multiplier thing which I don't feel like typing out.

The Attempt at a Solution



I'm attempting to separate the equation so I can have y and dy on one side and x and dx on the other, but the denominator is making that really hard for me to do. Any ideas on how to separate it? Thanks.
 
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Something like u=y/x and so y' = xu'+u. Divide the numerator and denominator of RHS by x^2 to get into the u form. Just make sure you substitute away all the y and y' terms.
 

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