`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.