There are 6 equations there, it appears to me.
You indicate that only u,v,w,x,y,z and t are variables are variables, but you show u' and v' and so on, which implies that u, v,w, x, y, and z are functions rather than variables.
Is y2 a constant or is it y^2 ?
Is ∂L/∂u the derivative of L with respect to u? If it is then that implies you have at least 7 functions (but only 6 equations)
Is sgn(v) the sign() function applied to v? If it is, then what value is sgn(0) ? Some places define sgn(0) as NaN and some define it as 0 and some define it as 1.
Your definition of x' starts with 1/m2[EXPRESSION] . Are we to take that as (1/m2)*(EXPRESSION), or are we to take that as 1/(m2*(EXPRESSION)) ?
As you have some variables that appear to be constructed of more than one character, we cannot tell whether cv is a single constant or if it is instead c*v .
Is 2∂L/∂uv 2*v*diff(L(t),u(t)) ? Or is it 2*diff(L(t),u(t)*v(t)) ?
Is ∂^2 L intended to be diff(L(t),t,t) ?
Please rewrite your expressions in full operator notation, using * for all multiplications, and converting all characters such as μ and ∂ to characters that are valid in MATLAB expressions, and converting all function calls to their MATLAB equivalents. Use () when necessary, but do not use [] or else we will interpret that portion as being the construction of a vector.
If ∂ is the differential operator, then since u is really u(t), a function rather than a variable, ∂L/∂u would have to be the differential of one function with respect to a second function. In such a case, you would not have ODE: you would have PDE, it seems to me.
