y' + (-1+x^2)y' - 2xy = 0 Solve the differential equation

To solve this differential equation, we'll try to separate the variables: move y and y' to the left side and x without y to the right:
y'(1 + x^2 - 1) = 2 x y,  or  (y')/y = (2x) / x^2 = 2/x.
Now we can integrate both sides with respect to x and obtain
ln|y| = 2ln|x| + C,
which is the same as
y = Ce^(2 ln|x|) = C |x|^2 = C x^2,
where C is an arbitrary constant. This is the general solution.