The equation of the curve satisfying the differential equation `y((dy)/(dx))^2+(x-y)(dy)/(dx)-x=0` can be a (a) circle (b) Straight line (c) Parabola (d) Ellipse

Options

A. Circle
B. Straight line
C. Parabola
D. Ellipse

Answer

A, B

Explanation

`y((dy)/(dx))^(2)+(x-y)(dy)/(dx) -x=0`
or `(dy)/(dx) = ((y-x)+-sqrt((x-y)^(2)+4xy))/(2y)`
So, `(dy)/(dx)=1` which gives straight line.
or `(dy)/(dx)=1` which gives straight line
or `(dy)/(dx)=-x/y` which gives circle.