There is a simple differential equation $ y''(x) + (\varepsilon - x^2) y(x) = 0 $. If one uses the new variable $ x^2 = s $, using the chain rule, this differential equation becomes $ 4 s y''(s) + 2 y'(s) + (\varepsilon - s) y(s) = 0 $. Now, I want to do it in Mathematica. I define the differential equatrion as
diff[x_] := y''[x] + (ε - x^2) y[x]; Simplify[diff[x] /. x^2 -> s]
But, it does not work. How can I figure it out?