Electric field with Maxwell's 1st equation

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With a total charge Q within a radius R the problem is to find the electric field at a radius r>R and r<R. The charge density is within the radius R proportional to 1 / r and zero outside (uniform charge distribution both in-and outside R).

I'm trying to use Maxwell’s 1st equation: Coulomb’s law , but struggling getting it right and I think there are some facts missing for me.