Help needed for solving 2nd order differential equation

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Discussion Overview

The discussion revolves around solving a second-order differential equation of the form y'' + Ay' + By + Cy^2 = f(x), where y is a function of x. The context includes its application to a non-linear spring-mass-damper system with variable spring stiffness. Participants explore both analytical and numerical methods for finding solutions.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant requests assistance in solving a specific differential equation related to a physics problem.
  • Another participant suggests that the discussion should be moved to the math forum, indicating a potential mismatch in topic focus.
  • A participant clarifies that the differential equation applies to a non-linear spring-mass-damper system where spring stiffness is linearly proportional to displacement.
  • Some participants propose that due to the non-linear nature of the differential equation, a numerical solution may be more appropriate.
  • One participant inquires about the possibility of solving the equation analytically using the method of successive approximations, suggesting a potential form for the solution involving cosine terms.
  • Another participant agrees that while a numerical solution is likely necessary, an analytic solution might be possible for specific parameter values and functions.

Areas of Agreement / Disagreement

Participants generally agree that the non-linear nature of the differential equation complicates finding a solution, leaning towards numerical methods. However, there is some debate about the feasibility of finding an analytical solution under certain conditions.

Contextual Notes

The discussion highlights the complexity of the differential equation and the potential limitations in finding a general analytical solution, depending on specific parameters and the function f(x).

kemiao
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can someone help me solve the differential equation that takes the following form?

y''+Ay'+By+Cy^2=f(x), y is function of x

Thanks a lot!
 
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Move to math forum - diff. eq.
 
thanks, it actually applies to a specific physics problem

thanks. it actually applies to a specific physics problem.
i am trying to solve this for a non-linear spring-mass-damper system where the spring stiffness is not constant, but linearly proportional to displacement. thanks!
 
Since the DE is non-linear, a numerical solution would probably be called for.
 
thanks a lot. is there a way to solve it analytically using method of successive approximations?
i'd imagine the solution could take a form of something like
y(x) = A1*cos(x)+A2*x^2*cos(2x)+A3*x^3*cos(3x)+...

SteamKing said:
Since the DE is non-linear, a numerical solution would probably be called for.
 
SteamKing said:
Since the DE is non-linear, a numerical solution is probably called for.

Agreed. You might be lucky and find an analytic solution for particular parameter values and a particular f(x), but a general analytic solution is probably not possible.
 

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