From the differential equation by eliminating A and B in `Ax^(2)+By^(2)=1`

Explanation

Differentiating `Ax^(2) + By^(2) =1`
twice w.r.t .x, we get ,
` 2Ax + 2By (dy)/(dx) =0`
i.e, ` Ax + By (dy)/(dx) =0`
` and A+ B [ y (d^(2)y)/(dx^(2))+ (dy)/(dx)/ (dy)/(dx)]=0`
`A+ B [ y (d^(2)y)/(dx^(2))+((dy)/(dx))^(2)] =0`
These there equations in A and B are consistent determinant of their consistency is zero.
`|{:(x^(2),y^(2),1),(x,x(dy)/(dx),0),(1,y(d^(2)y)/(dx^(2))+ ((dy)/(dx))^(2),0):}|=0`
` x^(2)(0-0)-y^(2) (0-0)+1 [xy (d^(2)y)/(dx^(2))+x ((dy)/(dx))^(2)-y(dy)/(dx)]=0`
`xy(d^(2)y)/(dx^(2)) +x((dy)/(dx))^(2) -y (dy)/(dx)=0`
The is the required D.E.