With this definition of k , the position- or x -dependent part will appear as ± ± j k x in the exponential solutions of the equation, similar to the time-dependent part + j ω ω t so the solution reads V ( x ) = v ( + ) e − − j k x + v ( − − ) e + j k x where v ( + ) and v ( − − ) are the constants of integration for the forward moving (+) and backward moving (−) waves, as in the prior section. When we recombine the time-dependent part we obtain the full solution: V ( x , t ) = V ( x ) e + j ω ω t = v ( + ) e − − j k x + j ω ω t + v ( − − ) e + j k x + j ω ω t .