All separable equations are exact?

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SUMMARY

The discussion centers on the mathematical proof that the separable equation dy/dx = M(x)N(y) can be expressed as an exact equation. The correct formulation is M(x)dx - N(y)dy = 0, which confirms its exactness. Participants clarify the transformation from the separable form to the exact form, emphasizing the importance of proper notation in differential equations.

PREREQUISITES
  • Understanding of differential equations
  • Familiarity with exact equations
  • Knowledge of separable equations
  • Basic calculus concepts
NEXT STEPS
  • Study the properties of exact differential equations
  • Learn about the conditions for exactness in differential equations
  • Explore the method of integrating factors for non-exact equations
  • Review examples of separable equations and their transformations
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Students and professionals in mathematics, particularly those studying differential equations, as well as educators looking to enhance their understanding of exact and separable equations.

epiclesis
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How can I show that the separable equation dy/dx = M(x)N(y) is also exact?

Any ideas?

Thanks in advance!

-epiclesis
 
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dy/dx = M(x)N(y) implies
M(x)dx - dy/N(y) = 0
is this equation exact?
 
Last edited:
Of course, that should be "M(x)dx- N(y)dy= 0".
 

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