- #1

However, in general this doesn't appear to be a valid strategy. If I have the equation ##4x - 3y = \frac{dy}{dx}##, and rewrite this as ##\int (4x - 3y) dx = \int dy##, I can't then just hold ##y## constant on the left when I integrate both sides since evidently I'll get the wrong answer. Some other strategy needs to be used.

So why is it only permitted in some instances to hold certain variables constant? Thanks for your help!