In this articlehttp://arxiv.org/abs/0802.3525, the authors present the inhomogeneous equation(adsbygoogle = window.adsbygoogle || []).push({});

$$\ddot{\phi}_2 + \phi_2 + g_2\phi_1^2 + \omega_1\ddot{\phi}_1 = 0\tag{11}$$

followed by its solution

$$\phi_2 = p_2\cos(\tau + \alpha) + q_2\sin(\tau + \alpha) + \frac{g_2}{6}p_1^2[\cos(2\tau + 2\alpha) - 3] + \frac{\omega_1}{4}p_1[2\tau\sin(\tau + \alpha) + \cos(\tau + \alpha)]\tag{14}$$

How is this solution obtained?

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# How is this equation solved?

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