求齐次方程y(x^2-xy+y^2)dx+x(x^2-xy+y^2)dy=0求其通解

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求齐次方程y(x^2-xy+y^2)dx+x(x^2-xy+y^2)dy=0求其通解求齐次方程y(x^2-xy+y^2)dx+x(x^2-xy+y^2)dy=0求其通解求齐次方程y(x^2-xy+y^

求齐次方程y(x^2-xy+y^2)dx+x(x^2-xy+y^2)dy=0求其通解
求齐次方程y(x^2-xy+y^2)dx+x(x^2-xy+y^2)dy=0
求其通解

求齐次方程y(x^2-xy+y^2)dx+x(x^2-xy+y^2)dy=0求其通解
y(x^2-xy+y^2)dx+x(x^2-xy+y^2)dy=0
(x^2-xy+y^2)(dxy+dxy)=0
(x^2-xy+y^2)*2dxy=0
2dxy=0(1)或者x^2-xy+y^2=0(2)
由(1),得
x=0,或y=0
由(2),得
(x-y/2)^2=-3/4y^2,x=y=0