Linear Differential Equation Help

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SUMMARY

The discussion focuses on solving the linear differential equation y + (3 + 3x - y)dy/dx = 0. The key solution involves using the integrating factor μ = y² to transform the equation into an exact differential equation. This allows for the application of standard methods for solving exact equations, as outlined in the referenced Wikipedia articles on inverse functions and exact differential equations.

PREREQUISITES
  • Understanding of linear differential equations
  • Familiarity with integrating factors
  • Knowledge of exact differential equations
  • Basic calculus concepts, particularly differentiation
NEXT STEPS
  • Study the method of integrating factors in differential equations
  • Learn about exact differential equations and their solutions
  • Explore the concept of inverse functions in calculus
  • Practice solving linear differential equations with various integrating factors
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Students and professionals in mathematics, particularly those studying differential equations, as well as educators looking for examples of solving linear differential equations.

tylercollins
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This is a question I have been staring at for a while now. I can't figure it out for the life of me.

'Solve the following equation that is linear in x: y + (3 + 3x - y)dy/dx = 0

I don't even know where to start. Any help would be greatly appreciated.
 
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The equation becomes exact if you multiply both sides by the integrating factor μ = y2.

You can then find the solution using regular methods for solving exact equations.

http://en.wikipedia.org/wiki/Exact_differential_equation.

Not sure if Wikipedia explains the method very well, but just so you have an idea of what I'm talking about :)
 

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