I do get smooth plots:
{sol1, sol2} =
NDSolveValue[{y1'[x] + 4 y1[x]/x ==
0, (4 y2'[x])/x + (10^-36 x^6 y2[x] + 1/2 y1'[x]*y2'[x])/y1[x] +
y2''[x] == 0, y1[1] == 10^33, y2'[1] == 0, y2[1] == 10^8}, {y1,
y2}, {x, 10^0, 10^7}, MaxSteps -> 10000000]
Plot[sol1[x], {x, 1, 3}, PlotRange -> All]
Plot[sol2[x], {x, 1, 6000000}]
Plot[sol2[x], {x, 1000000, 2000000}]