We know that if we have a lagrangian like $$L(\dot{q}_1, \dot{q}_2, q_1 ,q_2 )=(\dot{q}_1q^2_1 + \dot{q}^2_2 + q_1^2 - q_2^3)$$ then we can get the equations of the motion i.e. $$q_1 =0\\ 2\ddot{q}^2_2 + 3{q}^2_2 = 0$$ using the Euler-Lagrange equations.
My question is about the converse of this statement: If one knows the equations of motion, like the above equation, then how can I calculate the lagrangian L (or equivalent lagrangians)?