Solve Nonlinear ODE Symbolically

Question

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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?