Solving Non-Homogeneous Differential Equations with Two y' Terms

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Homework Help Overview

The discussion revolves around solving a non-homogeneous differential equation involving two terms of y', specifically in the context of the equation (y-xy')^2=x^2+y^2. The original poster expresses familiarity with homogeneous equations but finds this case challenging due to the presence of two y' terms.

Discussion Character

  • Exploratory, Problem interpretation

Approaches and Questions Raised

  • Participants explore the implications of taking the square root of both sides of the equation and consider how this might simplify the problem. There is also a suggestion to express the equation in the form y'=f(x,y) to facilitate solving.

Discussion Status

The discussion is ongoing, with participants offering hints and exploring different interpretations of the problem. Some guidance has been provided regarding the transformation of the equation, but no consensus or resolution has been reached.

Contextual Notes

The original poster has indicated a focus on hints rather than complete solutions, suggesting a desire to engage with the problem-solving process actively.

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Homework Statement



I have to find the differential of (y-xy')^2=x^2+y^2.Now,I have solved hom. equations but this is different because there are two y'. I know how to prove that it is a hom. equation of degree zero, so we can skip that, but how to solve this? Some hints would be highly appreciated.

Homework Equations





The Attempt at a Solution

 
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What happens if you take the square root of both sides of the equation?
 
(y-xy')=sqrt(x^2+y^2)
 
Do you know how to solve homogeneous equations of the form y'= f(x,y)?

Can you write (y-xy')=sqrt(x^2+y^2) as y'=f(x,y)?
 

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