令y/x = u
du = 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 + tanu
cosudu/sinu = dx/x
积分得
ln|sinu| = ln|x| + C
即sinu = kx,或写作sin(y/x) = kx
解方程：dy/dx=y/x+tan(y/x)
令y/x = u
du = 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 + tanu
cosudu/sinu = dx/x
积分得
ln|sinu| = ln|x| + C
即sinu = kx,或写作sin(y/x) = kx