How can I solve a non-homogeneous equation using substitution?

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SUMMARY

The discussion centers on solving a non-homogeneous equation using substitution, specifically the substitution of y=zx. The user initially attempted to solve a homogeneous equation but encountered difficulties due to the presence of non-homogeneous terms, specifically "+1" and "-1". The challenge lies in effectively separating the variables after substitution. The community provides insights on addressing these non-homogeneous components to facilitate a solution.

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  • Understanding of differential equations and their classifications
  • Familiarity with substitution methods in solving equations
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  • Basic calculus concepts, including derivatives
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Joe20
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Hi, I have attached part of my steps for solving the homogeneous equation.
The equation is proven to be homogeneous. However after using substitution of y=zx and its' derivative, I was not able to separate the variables conveniently as shown. Please advise. Thank you!
 

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The difficulty is that this equation is NOT homogenous because of the "+ 1" and "-1" terms.
 

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