Question

Use the initial condition to find the particular solution of the differential equation.
Differential Equation Initial Condition
yy' − ex = 0 y = 8 when x = 0

Answer 1

i don't really know this stuff, but can't you start with
\[\int y y' =\int e^xdx\]?

Answer 2

As satellite mentioned, you can separate the variables and integrate:
\[\int y\,dy=\int e^x\,dx\]
(Close enough :P)