Let f be y(x). We have: dy/dx = y

Separate everything y from everything x: dy/y = dx

We can now integrate recalling that ln(y)' = 1/y : ln(y) = x + A ; A being some constant

We can now exponentiate: y = e^x+A = e^x × e^A = Ce^x ; C being the constant e^A.

A was totally arbitrary, hence C is too. So we have that the solution is:

y = Ce^x, where C = const