Answer to Question #59071 in Differential Equations for ABJ

Question

7 Obtain the differential equation associated with the given primitive
lny=Ax^2 + B, A and B being arbitrary constants.
(I) xy(d^2y/dx^2) – y dy/dx − x(dy/dx)^2=0
(II) xy (d^2y/dx^2) − 2y dy/dx=0
(III) 3xy (d^2y/dx^2) + 2y dy/dx − x(dy/dx)^2 =0
(IV) Xy (d^2y/dx^2) − x(dy/dx)^2=0
8 Solve y(xy+1)dx+x(1+xy+x^2y^2)dy=0
(I) 3x^2y^2lny−2xy−3=Cx^2y^2
(II) 2x^2y^2lny−2xy−1=Cx^2y^2
(III) 2x^2y^2lny−xy=Cx^2y^2
(IV) 2x^3y^2lny−2xy−1=Cx^2y^5