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I have a differential equation and when I try to solve it by using the "NDSolve" command, the Mathematica gives an error. The differential equation and error are as follows

NDSolve[{Y''[a] + 51/20 Y'[a]/a - 9/20 a^-3 Y[a] == 0, Y[1] == 1, 
Y'[1/1000] == 1}, Y, {a, 1/1000, 1}]

NDSolve: At a == 0.001`, step size is effectively zero; singularity or 
stiff system suspected.

I will be thankful if someone help.

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  • $\begingroup$ Cannot reproduce the mentioned warning in v11.3 and v12. Which version are you in? $\endgroup$ – xzczd Oct 4 at 6:21
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DSolve[{y''[a] + 51/20 y'[a]/a - 9/20 a^-3 y[a] == 0, y[1] == 1, 
  y'[1/1000] == 1}, y, {a, 1/1000, 1}]

enter image description here

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NDSolve[{Y''[a] + 51/20 Y'[a]/a - 9/20 a^-3 Y[a] == 0, Y[1] == 1, 
Y'[1/1000] == 1}, Y, {a, 1, 1/1000}, WorkingPrecision -> 24]
Plot[Evaluate[Y[a] /. %], {a, 1, 1/1000}]

enter image description here

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