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If both definitions of sys3 are intended to be equivalent, you made a sign error. xmax = 2; sys31 = {y'[x] == 2 y[x]/(1 + y[x]^2) - Exp[y[x]]/(1 + Exp[y[x]]), y [0] == 1} (* {Derivative[1][y][x] == -(E^y[x]/(1 + E^y[x])) + (2*y[x])/(1 + y[x]^2), y[0] == 1} *) soln1 = NDSolve[sys31, y, {x, 0, xmax}][[1]]; sys32 = {y'[x] - 2 ...



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