how do i show something is a solution without solving it? 2nd order DE

the wave equation

δ^{2}y/δx^{2} = (1/c^{2})(δ^{2}y/δt^{2})

show y(x,t) = f(x-ct)+g(x+ct) is a solution __explicitly__

please show me how, don't just say "substitution"

Re: how do i show something is a solution without solving it? 2nd order DE

Quote:

Originally Posted by

**ouchimdead** don't just say "substitution"

Ahem...

Anyway, just in case a picture helps...

http://www.ballooncalculus.org/draw/...rtial/five.png

... where (key in spoiler) ...

Compare bottom rows.

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