I just took an exam and the final problem was the following: dy/dx = (y-3) e^(cos(xy)) y(1)=1 prove that y(x) < 3 for all x for all y that are defined. To be honest, I tried a few things but realized I didn't know where to start. I can show that the limit of the slope from neg. infinity to infinity is zero which means 3 is an asymptote but I had no idea how to show this. Ideas?