Verified answer

this is a separation of variables problem

multiply by dx on both sides, and move e^y over to the other side

-e^y dy = (6 - x) dx (divide by negative 1)

e^y dy = (x - 6) dx

Integrate both sides...left side with respect to y...right side with respect to x.

e^y = x^2/2 - 6x + C

use the inital value conditions to solve for the constant.