Well, if , then .
kills of all functions of t.
Hi all,
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,
ArTiCk
This is simply wrong. You cannot "factor" derivatives like that.
You can write it as which says that is independent of x. That is, that where F(t) can be any function of t only.
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