This is my first question on this forum, so I apologize if I am not very clear.
We have this exercise about three-dimensional harmonic oscillators and there's this differential equation I simply don't understand. It's $$\frac{d^2u}{d \rho^2} \approx u\rho^2\rho_0^2$$ and the general solution should be $$u(\rho)\approx Ae^{-\frac{\rho_0\rho^2}{2}}+Be^{\frac{\rho_0\rho^2}{2}}$$
Does anyone understand this, and if so could they explain it?
Thank you.