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2nd order PDE- general solution

Hi all,

I am trying to determine the general solution for the following equation:

http://www.mathhelpforum.com/math-he...1&d=1257775597

First of all i factorised it and determined the 1st order ODEs to be:

http://www.mathhelpforum.com/math-he...1&d=1257775955

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,

ArTiCk