What type of ordinary differential equation is the following equation:?

Question

Is it a homogeneous, exact, separable, linear, bernoulli, etc. and how do you solve?

dy/dx= -(2x+1/y)/(1/y-x/(y^2))

Answer 1

You would need to simplify the expression but by inspection (and subsequent simplification and editing) - I think you have a non-separable and non-linear system.

Answer 2

And since non-linear, also non-homogeneous.

Answer 3

it is a non-linear but non-circle, non-parabola, non-trig function graph