(x^2+y^2+x)dx+xydy=0积分因子及积分求解

2025-02-26 15:43:40
推荐回答(1个)
回答1:

d(x^2+y^2+x)/dy=2y
d(xy)/dx=y
(2y-y)/xy=1/x
e^[∫(1/x)dx]=x(积分因子)
(x^3+xy^2+x^2)dx+yx^2dy=0
x^4/4+x^3/3+(y^2)d(x^2)/2+(x^2)d(y^2)/2=0
x^4/4+x^3/3+(x^2)(y^2)/2=C