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I want to obtain y(x) of following answer with Mathematica:

root

and my code is 

Clear[y, λ, x, z, u, v]
eqn = y''[x] == λ *x*y[x]/Sqrt[-1 + x]
u[x_] := Sqrt[-1 + x]
y[x_] := z[u[x]]
eqn2 = Simplify[eqn /. x -> InverseFunction[u][v], v > 0]
zSolution[v_] = z[v] /. First[DSolve[eqn2, z[v], v]]
ySolution[x_] = zSolution[u[x]]
J. M.'s missing motivation
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Bahram Agheli
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    As I commented below the answer from which this question is derived, what you're getting is a solution in the form of a function that has to be numerically evaluated. Not every differential equation can be solved in terms of named special functions. Maybe if you make additional assumptions about boundary conditions you could get a simplification, in particular if you put those boundary conditions in to DSolve from the start. But as it stands, there's probably nothing better available within Mathematica. Provide all known assumptions. – Jens May 01 '15 at 16:44
  • I added the direct NDsolve approach to the other question. If that's all you need then all this variable substitution is a lot of work for no benefit. – george2079 May 01 '15 at 20:05
  • I use your answer, but I obtain again "DifferentialRoot". My question change to the following differential equation: eqn = y''[x] == λ x y[x]/Sqrt[-1 + x] – Bahram Agheli May 02 '15 at 06:48

0 Answers0