Hamilton vs. Lagrange

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Hamilton's Equations of Motion \begin{align} \frac{\partial H}{\partial p_i}=\dot{q}_i \end{align} \begin{align} -\frac{\partial H}{\partial q_i}=\dot{p}_i \end{align} Lagrange's Equations of Motion \begin{align} \frac{\partial L}{\partial \dot{q}_i}=p_i \end{align} \begin{align} \frac{\partial L}{\partial q_i}=\frac{d}{dt}\frac{\partial L}{\partial \dot{q}_i}=\dot{p}_i \end{align}