Nonlinear second order differential equation

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SUMMARY

The discussion centers on solving the nonlinear second order differential equation represented as ay'' + b|y|y' + cy + dx = 0. Participants suggest numerical methods for obtaining solutions, as analytical solutions are challenging. Additionally, transforming the equation into a first order system is recommended to facilitate the solving process. Asymptotic analysis is also mentioned as a potential approach for understanding the behavior of solutions.

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  • Basic concepts of asymptotic analysis
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  • Research numerical methods for solving nonlinear differential equations
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Graduate students, researchers in applied mathematics, and anyone involved in solving complex differential equations will benefit from this discussion.

Ioria
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Hello!
It is the first time that i write on this forum. I'm doing a PhD but i can't solve this equation:
it's a non-linear second order differential equation.

ay''+b|y|y'+cy+dx=0

Some ideas?
 
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No idea analytically, but have you tried numerically solving it? That way you can get an idea of what it look like and then perhaps asymptotic analysis.

Have you tried writing it as a first order system?
 

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