Non linear second order differential equation with non costant coefficients

Hello everybody,

I have a problem with differential equations. My problem is related to a second order, non linear system of differential equation with non constant coefficient. The problem is write the function to feed the ode solver that takes into account for each time step the new value of the coefficient. I will write the equations of the system, where the dx1 denotes first derivative of the variable x1 and ddx1 second derivative of the variable x1.

a11*ddx1+a13*ddx3+a15*ddx5=-b11*dx1-b13*dx3-b15*dx5+F1(t)    
a33*ddx3+a35*ddx5+a31*ddx1=-b33*dx3-c33*x3-b35*dx5-c35*x5-b31*dx1+F3(t)
a55*ddx5+a51*ddx1+a53*ddx3=-b55*dx-c55*x5-b51*dx1-b53*dx3-c53*x3+F5(t)
ddx6*(T+x6+aw11)+ddx3(T+x6+aw11)=-dx6*abs(dx6)-((dx6)^2)-g(x6+x3)+F6(t)

Above there is the system, all the coefficients are known, my problem is how should I write the system in the function, expecially for the fourth equation, where I do not know how isolate the the second derivative terms and I do not know how I should manage x6 that appears as a coefficient of ddx6 and ddx3. Any example or advice would be really really appreciated.

Thanking in advance Alessandro