This problem is out of Kreyszig's 9E of advanced engineering mathematics. I don't understand their closed form solution. Their solution ends up being y=3tan(3x+c)-9x. But when they were solving v=y+9x for y, then taking the derivative, they get: y'=v'-9, then set that =v^2 --Thats the step I have issues with. They are taking the derivative, but with respect to what? If it is some dummy variable, it would be y'=v'-9x' (chain rule?). If it is y with respect to v, the derivative of y=v-9x would just be y'=v'. Unless x' with respect to a dummy variable is = 1, of course. Can someone please enlighten me?