Question

When integrating D.E.s, is there a rule on which side the +c usually goes?

Answer 1

Normally, people put it on the right side, but that would depend on which side you're doing the actual integration

Answer 2

so if there's for example dy*y on the left and dx*x on the right side

Answer 3

See the c1 and c2 i brought in from integrating?
You can skip that step, and just combine them into 1 new constant if you want.
That's why we tend to just integrate 1 constant into the equation.

Because the constant is arbitrary (it represents all possible values of a constant, positive and negative).

So if you move c1 to the other side, it becomes -c1.. but c1 covers all possible constant values, including negatives.. so that's just another constant

If we combine that with another arbitrary constant, that gives us another arbitrary constant!
and we can just call it C instead of C1 and C2.

It will certainly start to matter when you start dealing with Second Order DE's and you need a constant for each solution :D

Sorry if that was long winded, just wanted to make sure you understood what's going on.