令y/x = udu = d(y/x) = (xdy-ydx)/x则dy/dx = (x du/dx + y)/x = xdu/dx + u代入原式代换xdu/dx + u = u + tanucosudu/sinu = dx/x积分得ln|sinu| = ln|x| + C即sinu = kx,或写作sin(y/x) = kx