where F is an arbitrary function of u.
Integrating we get
Thus, the general solution of the wave equation is
y = f (x – vt) + g (x + vt).
The waves ƒ (x – vt) and g (x + vt) travel with same velocity v, but in opposite directions. The wave ƒ (x – vt) is called forward wave which moves along the positive x-direction and the wave g (x + vt) is backward wave which moves in the negative x-direction. The method described here for solving the partial differential equation is known as D’ Alembert’s method.
