How to solve y''+y'/x+y=0 using B.C.s y(0)=0 and y'(0)=1

I have tried Dsolve,ode45,ode23,ode15s. But didn't prove any luck.

[Roger Stafford]

The reason for your trouble with the numerical ode’s is that initially at x = 0, you must have y” an infinite value to satisfy the equation y” + y’/x + y = 0. That is because y’/x is equal to 1/0 = infinity at that first point. This creates unsurmountable difficulties for the numerical ode procedures. You probably need to reconsider either those initial conditions or else the differential equation itself.

[Torsten]

In general, the solution to your ODE is

y(x)=const1*J_0(x)+const2*Y_0(x)

with J and Y being Bessel functions.

http://www.wolframalpha.com/input/?i=y''(x)+%2B+y'(x)%2Fx%2By(x)+%3D+0

Best wishes

Torsten.