Equation of Motion So I have an equation of motion with an additional viscous force shown below: $ \frac{d^2x}{dt^2} = x^3 - x^5 - \frac{dx}{dt} $ And the question is `Rewrite as a system for x(t) and v(t)`. I don't even understand how to begin this problem. Any ideas?

Let $\frac{\mathrm{d}x}{\mathrm{d}t}=\dot{x}=v$ and $\frac{\mathrm{d}^2x}{\mathrm{d}t^2}=\ddot{x}=\dot{v}$. The original equation can now be written as $\dot{v}=x^3-x^5-v$. In consequence, the second order differential equation has been replaced by a system of two first order differential equations, namely

$$\left\\{\begin{array}{l l} \dot{x}=v\\\ \dot{v}=x^3-x^5-v \end{array}\right.$$

Note that the derivatives depend only on $x$ and $v$.