2nd order PDE- general solution
I am trying to determine the general solution for the following equation:
First of all i factorised it and determined the 1st order ODEs to be:
For equation (1) there are no characterisitcs. While, for equation (2), i determined the characterisitics to be c_2 = x - t
The answer is.... the general solution,
phi(x,t) = F(t) + G(x -t)
Could some explain to me why there is F(t) in the general solution and why is it a function of t?
Thanks in advance,