I need to solve a system of 3 equations in the variable x1,x2,x3. Normaly I solve differential equations with ode solvers but in this system I have some problem with non linearity. I do not know how write the ode function that takes into account a term of a second order derivative of x2 in equation 1 or similar situations. I have a system of differential equation like that:

ddx1=(F1(t)-b11*dx1-a13*ddx3-b13*dx3-a15*ddx5-b15*dx5)/(m+a11)

ddx3=(F2(t)-b33*dx3-c33*dx3-a35*ddx5-b35*dx5-c35*dx5-a31*ddx1-b31*dx1)/(m+a33)

ddx5=(F3(t)-b55*dx5-c55*x5-a51*ddx1-b51*dx1-a53*ddx3-b53*dx3-c53*x3)/(I22+a55)

All the cofficients are known.

I do not know how write in the ode function for this system. Can somebody please explain or write an example of the ode function required to solve a non linear system like that? I would be grateful. I found a similar post where I wrote but I can not get the meaning.

Best regards Alessandro Antonini