微分方程式を解いて下さい(x^2y-y^3-y^2z)dx+(xy^2-x^3-x^2z)dy+(xy^2+x^2y)dz=0

(x^2y-y^3-y^2z)dx+(xy^2-x^3-x^2z)dy+(xy^2+x^2y)dz=0

(x^2y-y^3-y^2z)dx+(xy^2-x^3-x^2z)dy=0

f=x/y+y/x+z/x+z/y=c

(x^2y-y^3-y^2z)=λ(1/y-y/x^2-z/x^2)

λ=x^2y^2

xy^2+x^2y=x^2y^2(1/x+1/y+g)

g=0

df+0dz=0

f=c

--\u0026gt;

x^2+y^2+z(x+y)=cxy