作业帮dy/dx=(x+y^3)/xy^2
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dy/dx=(x+y^3)/xy^2
dy/dx=(x+y^3)/xy^2
dy/dx=(x+y^3)/xy^2
∵dy/dx=(x+y^3)/(xy^2)
==>xy^2dy=(x+y^3)dx
==>y^2dy/x^3=dx/x^3+y^3dx/x^4 (等式两端同除x^4)
==>d(y^3)/(3x^3)+y^3d(1/(3x^3))+d(1/(2x^2))=0
==>d(y^3/(3x^3))+d(1/(2x^2))=0
==>y^3/(3x^3)+1/(2x^2)=C/6 (C是常数)
==>2y^3+3x=Cx^3
∴原方程的通解是2y^3+3x=Cx^3.
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