1. The problem statement, all variables and given/known data So this is part of a broader problem about the quantum harmonic oscillator, but there's one particular bit of mathematics I'm stuck on. We have the differential equation: y''(x) +(ε-x2) y = 0 And I'm told that we're to examine how y behaves as x tends towards infinity. I took this to mean that we can ignore the term in epsilon entirely. We're also told that in this limit, we should obtain y = A xk e-x2/2 as the solution to the differential equation. 2. Relevant equations 3. The attempt at a solution I'm not entirely sure how to go about solving the differential equation (bit rusty) but when I substitute in the given solution, the "xk" term doesn't cancel as I suspect that it should - unless of course you just set k = 0, but the next parts of the question require we prefix it with A x^k . I'm confused.