大佬们，微分方程解到这不会解这个不定积分了，求大佬给解下

dy/dx = 1/(xy+y^3)
dx/dy = xy +y^3
dx/dy - xy =y^3
e^[-(1/2)y^2].[dx/dy - xy] =y^3.e^[-(1/2)y^2]
d/dy{ e^[-(1/2)y^2].x } =y^3.e^[-(1/2)y^2]
e^[-(1/2)y^2].x
=∫y^3.e^[-(1/2)y^2] dy
=-∫y^2. de^[-(1/2)y^2]
=-y^2.e^[-(1/2)y^2]+ 2∫ y.e^[-(1/2)y^2] dy
=-y^2.e^[-(1/2)y^2] -e^[-(1/2)y^2] +C
x=-y^2-1 +Ce^[(1/2)y^2]