I have succesfully plotted the running of the gauge couplings to one loop order with mathematica. My code is as follows: SMbetafunctions = {g1′[t] == 1/(16*Pi^2)*(41/6)*g1[t]^3, g2′[t] == 1/(16*Pi^2)*(-19/6)*g2[t]^3, g3′[t] == 1/(16*Pi^2)*-7*g3[t]^3, g1[0] == 0.35940, g2[0] == 0.64754, g3[0] == 1.1666}; sol = NDSolve[SMbetafunctions, {g1, g2, g3}, {t, 0, 50}]; Plot[Evaluate[{g1[t], g2[t], g3[t]} /. sol],Read more