The spherical Bessel equation is $$\left[\frac{d^2}{d\rho^2} +\frac{2}{\rho}\frac{d}{d\rho} - \frac{l(l+1)}{\rho^2} + 1\right] j_{l}(\rho) = 0$$ and I have the recurrence relation $$j_{l+1} = \frac{lj_{l}}{\rho} -\frac{dj_{l}}{d\rho}$$ and dont really know where to go from here.
In essence, I'd like to show: $$\left[\frac{d^2}{d\rho^2} +\frac{2}{\rho}\frac{d}{d\rho} - \frac{(l+1)(l+2)}{\rho^2} + 1\right] j_{l+1}(\rho) = 0.$$