If x^2+1=y/(x-y'), where y'=dy/dx, find dy/dx
I have tried so many ways, but I cannot seem to get the correct answer.
The answers I have got previously are:
x² + 1 = y/(x - y')
(x² + 1)(x - y') = y
x(x² + 1) - y'(x² + 1) = y
x(x² + 1) - y = y'(x² + 1)
dy/dx = x - y/(x² + 1)
x – dy/dx = y / (x² + 1)
Now switch sides:
dy/dx = x - y / (x² + 1)
dy/dx= (x³ + x – y) / (x² + 1)
However, both of them do not seem correct.
Any suggestions are welcome.
Also, I think that this is a linear ode. Even if i was to think of this as separable function, I would not have a clue how to get y' on the other side, as I would have to expand the left side with (x-y').