Help with bernoulli differential equation

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SUMMARY

The discussion centers on solving the Bernoulli differential equation represented by y'=(x^2-y^2)/xy. The user attempted a substitution method by letting y=xv, which led to the function f(v)=1/v-v. The final solution derived is y=(±) [(x^4+c)^(1/2)]/[(x*2^(1/2)], although the user expressed uncertainty about the Bernoulli equation's classification in their homework context.

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  • Understanding of Bernoulli differential equations
  • Familiarity with substitution methods in differential equations
  • Knowledge of algebraic manipulation and solving for y
  • Basic calculus concepts, including derivatives
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  • Study the general form and properties of Bernoulli differential equations
  • Learn about substitution techniques for solving differential equations
  • Explore examples of solving y'=(x^2-y^2)/xy using different methods
  • Investigate the implications of the solution y=(±) [(x^4+c)^(1/2)]/[(x*2^(1/2)] in practical applications
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I need help with solving equation y'=(x^2-y^2)/xy as bernoulli differential equation.

I also tried to do it differently by plugging in y=xv, so I got f(v)=1/v-v.

Finally I got answer y=(+/-) [(x^4+c)^(1/2)]/[(x*2^(1/2)] but I still have no idea how to do it as bernoulli equation
 
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