Help needed for solving 2nd order differential equation

[kemiao]

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!

 

[mathman]

Move to math forum - diff. eq.

 

[kemiao]

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!

 

[SteamKing]

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

 

[kemiao]

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)+...

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

 

[pasmith]

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.