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I have been given the steady state diffusion equation in 1d spherical polar coordinates as;

D.1/(r^2).'partial'd/dr(r^2.'partial'dc/dr)=0

I know that the solution comes in the form c(r) = A+B/r where A and B are some constants. I just dont know how to get from here to there. I have tried doing differentiation by parts on the equation then integrating the result, with no success. I can form a second order differential equation of the form;

r^2.'partial'd2c/dr2 +2r'partial'dc/dr = 0

but again dont know where to go from here. Any help greatly appreciated!