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I can't understand why or how or what they did in the part with Kx. I am confused because I don't know how they are getting K is negative or find out the x is -x..There has to be 2 cases where x is positive and x is negative but they rule out x is positive and say K is negative and thus x is negative...:S I don't get that part.

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EDIT: Is it because e^x can never be negative that they said K has to be negative to cancel the other negative out? If K was positive then e^x never reaches -1 so is that the reason?

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We have:

$-1 = K = \pm e^C$

Since $K$ is negative, it can only be the case that we use the negative $-e^C$, since the exponential cannot be negative.

Note, had the initial condition been, $y'(1) = 1$, then we would have chosen $+ e^C$.

Is that clear?

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  • $\begingroup$ yup that is what I realized after I remembered the e^x graph $\endgroup$ – Raynos Apr 15 '13 at 6:19

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