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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:

A

$v$ satisfies the equation $v'-2xv+1=0$.

B

$v$ satisfies the equation $v'+2(y_1-x)v+1=0$.

C

$y_1(x)$ could be $y_1(x)=x$.

D

Both Choice 'B' and Choice 'C' are correct.