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Hans Dolhaine
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Here is the whole procedure dgl = f'[t] == k f[t] - c sol = f[t] /. DSolve[dgl, f[t], t][[1, 1]] /. C[1] -> u ff[u_] := Evaluate[sol] (*ff fulfills the diff equation*) D[ff[u], t] - (k ff[u] - c) // Simplify (*you have...
Number 2 is really amazing. I thought I saw it sometimes somewhere, and even a proof, but I did not find it again. It seems convergence is really fast. A code to get the expression nn = 3; ppp = Join[{Sqrt[2]}, hh[ Table[(z =...
Another solution is given here https://community.wolfram.com/groups/-/m/t/1732127?p_p_auth=8REGCx2W
In fact every number z[m_] := 2^(2 + 4 m ) + 1 for m element Integers is divided by 5 without rest (proof by induction).
@Gianluca : thanks for these hints @Honyi Zhao : are you sure everyting is correct in the book? I get different results: sJ = (\[HBar]/2) PauliMatrix /@ {1, 2, 3}; normal = {Sin[\[Theta]] Cos[\[Phi]], Sin[\[Theta]] Sin[\[Phi]],...
Unfortunately, my stone-age version of FindRoot (version Mathematica 7) does not find solutions to your system of equations (singular jacobian). hmm. But, perhaps the following helps a bit Function to find its roots ff[x_, p_, q_] := (x -...
Note that you should change the integration-constants C[1] and C[2] in fs to K[1] and K[2] (or any others), that doesn't change the result. So you have 5 parameters: a, C[1], C[2], K[1] and K[2] in this sort of solution. I checked whether...
Perhaps like this? Integrate[x y z, {y, 0, 4}, {x, 0, 4}, {z, 0, 128 - y^2 - 4 x^2}]
Do you perhaps mean something like this? IntegratedDifferenceFunction[fi_, fo_] := NIntegrate[fi - fo, {x, 0, 2*Pi}] g1 = DSolve[{y''[x] + y[x] == 0, y[0] == .8, y'[0] == -.2}, y, x] g2 = DSolve[{y''[x] + y'[x] == 0, y[0] == .8,...