# How can I solve this differential equation?

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.

• Cannot reproduce the mentioned warning in v11.3 and v12. Which version are you in? – xzczd Oct 4 at 6:21

DSolve[{y''[a] + 51/20 y'[a]/a - 9/20 a^-3 y[a] == 0, y[1] == 1,

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