生例2求方程(y)y+8()x=0通解 解令Ⅱ=,则Ⅶ=xd+ydx, ∫(u)ydhx+g()x t-ydx≥0, lf(u)-(uld+g(udu=0, dx g(u) x ulf(u-g(u)l du=0, 通解为lmx|+ g(u) nf()-8/d"=C. 上页例2 求方程 f (xy) ydx + g(xy)xdy = 0 通解. 令u = xy, 则du = xdy + ydx, ( ) ( ) = 0, − +  x du ydx f u ydx g u x [ ( ) − ( )] dx + g(u)du = 0, x u f u g u 0, [ ( ) ( )] ( ) = − + du u f u g u g u x dx . [ ( ) ( )] ( ) ln | | du C u f u g u g u x = − + 通解为  解