Hi. Could somebody show me how to prove that has only one real root for ? All I know so far is that this equation has at least one root because for all real x.

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- Dec 16th 2012, 03:32 AMwilhelm**solved** Proof: the following equation has only one real root
Hi. Could somebody show me how to prove that has only one real root for ? All I know so far is that this equation has at least one root because for all real x.

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Already solved - Dec 16th 2012, 06:54 AMjakncokeRe: Proof: the following equation has only one real root
I got a solution that i thought was cool so im posting anyways. Now if . then and should be solutions to the differential eqn but for , we get implies so to have a solution to , x = 0 on the right side, so you get which for a > 1, has only 1 real root, namely