Second order nonlinear differential equation

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SUMMARY

The discussion focuses on solving the second order nonlinear differential equation y'' + ayy' + b = 0, where y is a function of x and 'a' and 'b' are constants. A participant suggests substituting y' = u, transforming the equation into a first order form. The key insight is to apply the chain rule to the term yy', allowing for direct integration to derive a first order equation. It is crucial to remember to include the arbitrary constant during integration.

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  • Understanding of differential equations, specifically second order nonlinear types.
  • Familiarity with substitution methods in differential equations.
  • Knowledge of the chain rule in calculus.
  • Ability to perform integration of functions.
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  • Study methods for solving second order nonlinear differential equations.
  • Learn about substitution techniques in differential equations.
  • Explore the application of the chain rule in calculus.
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vashistha
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hi,
i am facing problem in solving the following differential equation. help me.
y''+ayy'+b=0, where y is a function of x, 'a' & 'b' are constants.

i have tried substituting y'=u, which implies u'=u*dy/dx, these substitution change the equation to first order but i found no way ahead.
 
Last edited:
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To do this, recognize that you can reverse the chain rule on the term yy' to get (y^2/2)'. You can then directly integrate the equation to get a first order equation. (Don't forget the arbitrary constant that comes from doing so).
 

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