I need to solve the following system:
$$\left\{ \begin{array} { l l } { (u')^2 + (v')^2 = 1 } \\ {u'v'' - u''v' = uu' + vv' } \end{array} \right.$$
and it's a task that's proven to be quite hard by analythical methods. I had asked for help plotting the solutions to a similar system before, but I haven't been able to adapt the method to this case. My ultimate goal is to plot the curves given by:
$\alpha(s) = (\cos(u(s)), \sin(u(s)), v(s))$