速求微分y=xy`+y`+y`2的通解
问题描述：
速求微分y=xy`+y`+y`2的通解
答
y'-2xy=xy ,则y'=xy +2xy=xy(y+2).所以dy/[y(y+2)]=xdx 又1/[y(y+2)]=(1/2){(1/y)-[1(y+2)]}, 所以(1/2){(1/y)-[1
答
y=xy'+y'+y'2
y'=y'+xy''+y''+2y'y''
0=x+1+2y'
2y'=-(x+1)
2dy=-(x+1)dx
2y=-(1/2)(x+1)^2+2c
y=-(1/4)(x+1)^2+c