9. (15 points) A DC motor with motor constants $K_b$ and $K_t$ is driven by a bicycle wheel to power a headlight (resistor, $R_{light}$). Find an ODE, with dependent variable $v$ (voltage across the headlight), independent variable $t$ (time), and input $\omega_2(t)$ (angular velocity of bicycle wheel) to describe the system. Use the following model for the system.