例2求方程∫(xy)y+g(x)x=0通解 解令Ⅱ=x,则Ⅶ=xd+ydx, f∫(u)ydhx+g()x du-ydx =0 lf(u-g u)I-dx+g(udu=0, g(u du=o x ulf(u-g(u)l 通解为m|x|+ g(u) du= c ulf(u)-g(u)例2 求方程 f (xy) ydx + g(xy)xdy = 0 通解. 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 通解为 . [ ( ) ( )] ( ) ln | | du C u f u g u g u x = − +