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For a spherically symmetric mass density, the angular integral in spherical coordinates is $4\pi$. The two disjoint shell contributions therefore give the masssoBoth contributions are positive because $a<b$ and $c<d$.

The characteristic equation is $(r-1{)}^2=0$, so the repeated-root constant-coefficient differential equation gives the general solution $y=(A+Bx)e^x$. The first boundary condition gives $A=0$, and the second gives $B\pi e^{\pi }=\pi e^{\pi }$, hence $B=1$. Therefore