Homogeneous function of degree n

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SUMMARY

The discussion centers on the concept of homogeneous functions of degree n, specifically in the context of partial differential equations. The user seeks clarification on the definition and application of homogeneous functions, particularly in proving the equality of mixed partial derivatives, f_{xy} = f_{yx}. The user has successfully completed part a of their homework but expresses difficulty in progressing to part b due to perceived insufficient information in the problem statement.

PREREQUISITES
  • Understanding of partial differential equations
  • Familiarity with the concept of homogeneous functions
  • Knowledge of mixed partial derivatives
  • Basic calculus skills
NEXT STEPS
  • Research the definition and properties of homogeneous functions of degree n
  • Study the proof of equality for mixed partial derivatives
  • Explore examples of homogeneous functions in partial differential equations
  • Learn about the application of the Schwarz theorem in calculus
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Students studying calculus and differential equations, particularly those focusing on homogeneous functions and mixed partial derivatives.

athrun200
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Homework Statement


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Homework Equations





The Attempt at a Solution


I am learning partial differential and never be taught about homongeneous function.
What is this? How to solve the problem?
 

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I finally figure out how to do part a.
See my work on the photo.

Part b is similar to part a except 1 step.
That is, I need to prove [itex]f_{xy}[/itex]=[itex]f_{yx}[/itex]

It seems the question doesn't provide enough equation for me to do this.
 

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