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Main Question or Discussion Point
Are they both correct? Would the first or second solution be preferred?
Why is the second one not a solution? If you convert the original DE into an auxiliary equation, you will get roots: m_{1}=0 and m_{2}=k^{2}The second one is certainly not a solution. There is a solution in terms of exponentials, but that is not it.
No, the second is not correct.
Are they both correct? Would the first or second solution be preferred?
No you don't. You get roots of +k and -k. Try plugging your second solution into the DE and see if it works. You'll see that it doesn't.Why is the second one not a solution? If you convert the original DE into an auxiliary equation, you will get roots: m_{1}=0 and m_{2}=k^{2}
That's weird: http://www.wolframalpha.com/input/?i=m^2-k^2m=0No you don't. You get roots of +k and -k. Try plugging your second solution into the DE and see if it works. You'll see that it doesn't.