Integrating Factor: Need Help Solving Excersice?

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SUMMARY

The discussion centers on the mathematical concept of integrating factors in differential equations, specifically addressing the statement that if N is an integrating factor, then N*f(S) is also an integrating factor. Participants emphasize the importance of clarity in calculations and the necessity of using integrating factors correctly to transform non-exact differential equations into exact ones. The relevant equation discussed is dS = (dU + pdV) / N, highlighting the relationship between integrating factors and exactness in differential equations.

PREREQUISITES
  • Understanding of integrating factors in differential equations
  • Familiarity with exact and non-exact differential equations
  • Knowledge of differential calculus and its applications
  • Ability to manipulate and solve equations involving multiple variables
NEXT STEPS
  • Study the properties of integrating factors in differential equations
  • Learn how to identify exact and non-exact differential equations
  • Explore the method of solving differential equations using integrating factors
  • Review examples of applying integrating factors to specific differential equations
USEFUL FOR

Students studying differential equations, mathematicians interested in integrating factors, and educators teaching advanced calculus concepts.

B4cklfip
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Homework Statement
Show that if N is an integrating factor also N*f(S) is an integrating factor.
Relevant Equations
##dS = \frac{dU+pdV}{N}##
I'm not sure if that is the right way to solve this excersice. Can someone maybe help and tell me if this calculation proofs the statement ?

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B4cklfip said:
Homework Statement:: Show that if N is an integrating factor also N*f(S) is an integrating factor.
Relevant Equations:: ##dS = \frac{dU+pdV}{N}##

I'm not sure if that is the right way to solve this excersice. Can someone maybe help and tell me if this calculation proofs the statement ?

View attachment 263972
First off, ending with 0 = 0 doesn't do you any good.
Second, I'm having a hard time trying to follow what you're doing. Why are you introducing q in the 2nd line and dx and dy in the 3rd line?
What is the differential equation you're trying to solve? Is it Udx + Vdy = 0?
You are given that N is an integrating factor. How have you used it? The basic idea is that U(x, y)dx + V(x, y)dy = 0 is not an exact differential equation, multiplying by an integrating factor causes the new equation to be exact.
 

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