LinearAlgebra.SingularException(2) when solving matrix equation which is solvable in Maple

[dmbates]

@vikhes

dRdt = [2.7347115660463565e46 1.4462465159832052e46 7.06637105328182e46; 5.469423132092713e46 2.8924930319664105e46 1.413274210656364e47; -3.658477011433253e48 -1.9347779478036194e48 -9.453339201714811e48]
R = [1.0026696232160644e47, 2.0053392464321287e47, -1.3413640444362068e49]

dRdt\R

This returns the error

ERROR: LoadError: LinearAlgebra.SingularException(2)

I have tried to solve the equation in Maple and it solves it without an issue (see image below)

Does anyone know what is wrong?

The system is ill-conditioned

julia> dRdt = [2.7347115660463565e46 1.4462465159832052e46 7.06637105328182e46
               5.469423132092713e46 2.8924930319664105e46 1.413274210656364e47
              -3.658477011433253e48 -1.9347779478036194e48 -9.453339201714811e48];

julia> cond(dRdt)
2.885773849638737e32