First order differential equations

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SUMMARY

The discussion focuses on the approach to solving first-order differential equations, specifically the distinction between homogeneous and exact equations. It is established that when faced with an equation that exhibits characteristics of both, one should prioritize solving it as an exact equation due to the typically easier solution process. The user HallsofIvy provided valuable insights that clarified the confusion regarding the classification of these equations.

PREREQUISITES
  • Understanding of first-order differential equations
  • Knowledge of homogeneous and exact equations
  • Familiarity with the terms M(x,y) and N(x,y)
  • Basic problem-solving skills in calculus
NEXT STEPS
  • Study the characteristics of exact differential equations
  • Learn techniques for identifying homogeneous equations
  • Practice solving various first-order differential equations
  • Explore the implications of the degrees of M(x,y) and N(x,y) in differential equations
USEFUL FOR

Students and educators in mathematics, particularly those focusing on calculus and differential equations, as well as anyone seeking to improve their problem-solving skills in this area.

missmee
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good day everyone.
i need to know what test must i make first in dealing with differential equations.. please help me. it's hard for me to figure out whether an equation is homogeneous or exact... there are examples of exact differential equations that have same degrees for M(x,y) and N(x,y)..if that's the case, should i consider it as homogeneous before considering it as exact?
 
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Typically, it is easier to solve an "exact" equation than it is to solve a "homogeneous" equation so if I had an equation that was both, I would first try solving it as I would an exact equation.
 
HallsofIvy, thank you for your reply,. it helped me. :) Thank you. :)
 

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