# Determine characteristics for a PDE

Given the PDE $$\frac{\partial\rho}{\partial t} + 4 \frac{\partial\rho}{\partial x}= 0$$ determine the characteristics.

I understand how to solve this PDE using the method of characteristics as $$\rho=f(x-4t)$$, but I do not understand what is meant by "determine the characteristics".

Which equations are the characteristics?

In your case, the curve $$x(s), t(s)$$ such that $$\dfrac{dx}{ds} = 4 \\ \dfrac{dt}{ds} = 1$$