How can solve this nonlinear system?

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Someone help me to solve this system\begin{align*} \begin{cases} \ddot{x}_1(s) -\alpha \, x_1(s) \,\ddot{x}_2(s) &= 0 \\ \\ \ddot{x}_2(s) -\alpha \, x_1(s) \,\ddot{x}_1(s) - \alpha \, \dot{x}_1^2(s) &= 0 \end{cases} \end{align*}

Thank you in advance