\begin{align*}
\ddot{\theta}_1 &= \frac{-(l_1 \tau_2 \cos(\theta_1 - \theta_2) - l_2 \tau_1 + \frac{1}{2} g l_1 l_2 m_2 \sin(\theta_1 - 2\theta_2) + \frac{1}{2} \dot\theta_1^2 l_1^2  l_2 m_2 \sin(2\theta_1 - 2 \theta_2) + \dot\theta_2^2 l_1 l_2^2 m_2 \sin(\theta_1 - \theta_2) + g l_1 l_2 m_1 \sin \theta_1 + \frac{1}{2} g l_1 l_2 m_2 \sin \theta_1)}{l_1^2 l_2 (m_1 + m_2 - m_2 \cos^2(\theta_1 - \theta_2))} - \dot\theta_1 b \\
\ddot{\theta}_2 &= \frac{l_1 m_1 \tau_2 + l_1 m_2 \tau_2 - l_2 m_2 \tau_1 \cos(\theta_1 - \theta_2) + \dot\theta_1^2 l_1^2 l_2 m_2^2 \sin(\theta_1 - \theta_2) - \frac{1}{2} g l_1 l_2 m_2^2 \sin \theta_2 + \frac{1}{2} \dot\theta_2^2 l_1 l_2^2 m_2^2 \sin(2\theta_1 - 2\theta_2) + \frac{1}{2} g l_1 l_2  m_2^2 \sin(2\theta_1 - \theta_2) + \dot\theta_1^2  l_1^2 l_2 m_1 m_2 \sin(\theta_1 - \theta_2) - \frac{1}{2} g l_1 l_2 m_1 m_2 \sin \theta_2 + \frac{1}{2} g l_1 l_2 m_1 m_2 \sin(2\theta_1 - \theta_2) }{l_1 l_2^2 m_2 (m_1 + m_2 - m_2 \cos^2(\theta_1 - \theta_2))} - \dot\theta_2 b
\end{align*}