Difficult# Nonlinear First Order ODE: Riccati Equation

DIFFEQ-LEGHIY

Consider the Riccati equation:

$$y'=1+x^2-2xy+y^2$$

If $y_1$ is a solution, then we can try solutions of the form $y=y_1(x)+\cfrac{1}{v(x)}$. Determine which of the following statements are true: