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Take a solution that is independent of a parameter?

GROUPS:

Hi everybody. Please, I have to solve a system of equations with respect to a parameter and to take the only solution that is independent of another variable. This is the code. I think i had to better define the parameter k but i don't know how. This is the code

W[r_, l_] := e^2/(2*(l + 1)) - (l + 1)/r
V1[r_, l_] := W[r, l]^2 - D[W[r, l], r]
V2[r_, l_] := W[r, l]^2 + D[W[r, l], r]
a1 := l
a2[a1_] := a1 + k
Solve[D[V2[r, l] - V1[r, a2[a1]], r] == 0 && l >= 0 && r > 0 && 
  D[k[a1], a1] == 0, k[a1], Reals]

Thank you for your attention.

POSTED BY: deimos1990
Answer
11 days ago

I am not sure what you are asking. However, you should not use k and k[l] -- are they the same thing? If so, you may want

a2[a1_] := a1 + k[a1]
Solve[D[V2[r, l] - V1[r, a2[a1]], r] == 0, k[l]]

Which gives 2 solutions:

{{k[l] -> 1}, {k[l] -> -2 (1 + l)}}
POSTED BY: Updating Name
Answer
10 days ago

Thank you for the reply. I made a mistake in the code i wrote, i know. However the problem remain: i had to take the only solution that is independent from L but i solve the problem writing

ForAll[l,...]

Thank you!

POSTED BY: deimos1990
Answer
10 days ago

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