Question

First order partial differential equations examples

Answer 1

Answer:

A ∂u ∂x + B ∂u ∂y = C(x,y,u) into an “ODE,” i.e. a PDE containing only one partial derivative. If we plot the solution u(x,t) = f (x - vt) in the xu-plane, and animate t: f (x) = u(x,0) is the initial condition (concentration); u(x,t) is a traveling wave with velocity v and shape given by u = f (x).