Solve Nonlinear ODE Symbolically

I have the following non-linear ODE:

I have the following ODE45 solution:

fun = @(t,X)odefun(X,K,C,M,F(t),resSize); 
[t_ode,X_answer] = ode45(fun,tspan,X_0); 

The input matrices are stiffness K(X(t)), damping C, mass M, and force F. The nonlinearity is introduced by the spring stiffness matrix K(X(t)), where X(t) is a vector of the displacements of masses 1&2. That is, X(t) = [x1(t); x2(t)].

I would like to solve this ODE symbolically for expressions for x1(t) and x2(t). Can this be done with either ODE45() or dsolve()? Is there another better option that I'm missing?

Answer 1

[Torsten]

This is a nonlinear system of ODEs. An analytical solution with symbolic math is not possible.

The only way to solve it is numerically using one of the ODE integrators (e.g. ode45).