Find all the solutions of $\Delta u = u_{xx} + u_{yy} + u_{zz} = 0$ in three dimensions that depend only on $r = x^2 + y^2 + z^2$, the radial variable in polar coordinates. Use the following formula for ∆ in spherical polar coordinates $$u_{rr} + \frac{2}{r}u_r + \frac{1}{r^2}u_{\theta \theta} + \frac{1}{r^2}cot(\theta)u_{\theta} + \frac{1}{r^2 (sin\theta)^2}u_{\phi \phi }$$
I'm not sure how to start this problem. I'm thinking that $u_{rr} + \frac{2}{r}u_r = 0$ if $u$ is only to depend on r? Not sure how to continue