I am trying to solve the coupled differential equation numerically with Mathematica. But the range of values are large so mathematica cannot give correct plot. Here is the code:

`a = 4.75388*10^26; b = 5.424*10^-3; d = 4.75388*10^20; {X, Y} = {x, y} /. NDSolve[{x'[ z] == -((a/z) (x[z] - b*z^(3/2) E^(-z)) (BesselK[1, z]/BesselK[2, z])), y'[z] == ((d/z) (x[z] - b *z^(3/2) E^(-z)) (BesselK[1, z]/ BesselK[2, z]) - (a *z/4) (BesselK[1, z]) y[z]), x[0.1] == 1.552*10^-4, y[0.1] == 10^(-9)}, {x, y}, z] // FullSimplify // First LogLogPlot[{X[z], Y[z]}, {z, 0.1, 100}, PlotRange -> All] `