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I want to solve the following differential equation for $0 < x < 1$

DSolve[y''[x] == (λ x^(3/4) y[x])/Sqrt[1-x], y[x], x]
NSolve[y''[x] == (λ x^(3/4) y[x])/Sqrt[1-x], y[x], x]

But do not know how to actually solve it. Any suggestion?

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p = ParametricNDSolve[{y''[x] == (l x^(3/4) y[x])/Sqrt[1 - x], 
                      y[0] == 1, y'[0] == 1/2}, y, {x, 0, 1}, l]

Show@Quiet@Table[Plot[(y /. p)[l][x], {x, 0.1, 1}], {l, 1, 3}]

Mathematica graphics

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  • $\begingroup$ Can we have y[x] in terms λ? $\endgroup$ Jun 18, 2015 at 20:39
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    $\begingroup$ @Bahram I'm solving it numerically. I doubt there is a closed form $\endgroup$ Jun 18, 2015 at 20:40
  • $\begingroup$ @Bahram You can get things like Table[Plot[(y /. p)[l][x], {l, 0.1, 1}], {x, .1, .7, .1}], though $\endgroup$ Jun 18, 2015 at 20:42
  • $\begingroup$ @Dr.belisarius, How did you add those BCs ? $\endgroup$ Aug 22, 2019 at 7:12

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