In the case of time-independent H and ⁠ L ⁠, i.e. ⁠ ∂ ∂ H / ∂ ∂ t = − − ∂ ∂ L / ∂ ∂ t = 0 ⁠, Hamilton's equations consist of 2 n first-order differential equations, while Lagrange's equations consist of n second-order equations. Hamilton's equations usually do not reduce the difficulty of finding explicit solutions, but important theoretical results can be derived from them, because coordinates and momenta are independent variables with nearly symmetric roles.