Solve dydx=yx+tan(yx)\frac{dy}{dx} = \frac{y}{x} + \tan(\frac{y}{x})dxdy=xy+tan(xy) by substituting v=yxv = \frac{y}{x}v=xy. What is the resulting separable equation in vvv?
∫cot(v)dv=∫1xdx\int \cot(v) dv = \int \frac{1}{x} dx∫cot(v)dv=∫x1dx
∫tan(v)dv=∫1xdx\int \tan(v) dv = \int \frac{1}{x} dx∫tan(v)dv=∫x1dx
∫1vdv=∫1xdx\int \frac{1}{v} dv = \int \frac{1}{x} dx∫v1dv=∫x1dx
∫vdv=∫1xdx\int v dv = \int \frac{1}{x} dx∫vdv=∫x1dx