# 2nd order differential

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.

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?

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