I solved a pretty routine first-order diff. eq. where you simply separate the variables. xcos(x)(dy/dx) - sin(y) = 0 => [tex]\int cot(y)dy[/tex] = [tex]\int dx/x[/tex] Now, I thought that you would get an arbitrary constant, C, on both sides and they would cancel each other out, but that's wrong. My book lets e^C = A (why?). The answer should be sin(y) = Ax, but I didn't get that because I cancelled out the constant. I suppose my question is why does this happen?