## gerryliyana Group Title Second Order Differential Equations one year ago one year ago

1. gerryliyana Group Title

$y'' + \frac{ 1 }{ x }y'+ \left( 1-\frac{ n^{2} }{ x^{2} } \right)y = 0$ how much the solution zero-order of the Bessel equations above at (n=0) in between intervals of π along the positive x axis"????

2. kryton1212 Group Title

@ajprincess would you kindly help my brother if you are free....

3. ajprincess Group Title

I am extremely sorry @kryton1212.:( I havnt learnt differential equations yet.

4. kryton1212 Group Title

5. kryton1212 Group Title

if they learnt it *

6. ajprincess Group Title

@hartnn, @experimentX, @unklerhaukus, @apoorvk. Can u all plz help with this question?

7. kryton1212 Group Title

hartnn is not online yet...

8. ajprincess Group Title

But @unklerhaukus and @apoorvk are online. They may be able to help.:)

9. kryton1212 Group Title

thank you @ajprincess :)

10. ajprincess Group Title

Welcome:)

11. kryton1212 Group Title

12. UnkleRhaukus Group Title

can you reword the question, im not sure what you are asking

13. kryton1212 Group Title

@sauravshakya would you kindly help my brother if you are free?

14. gerryliyana Group Title

@UnkleRhaukus " how much the minimum solution of the equations above (at n=0) in between intervals of π along the positive x axis????"

15. UnkleRhaukus Group Title

i dont know what you mean by "how much the ..... solution?" are you looking for the number of solutions? are you looking for the solution? are you looking for the value of the function at one of the solutions?

16. gerryliyana Group Title

i'm looking for the least number of solutions..,

17. gerryliyana Group Title

the minimum number of solutions

18. UnkleRhaukus Group Title

ah ok.

19. experimentX Group Title

write it up as $x^2 y'' + xy' + (x^2-n^2)y = 0$ this is a standard non liner differential equation called Bessel differential equation http://en.wikipedia.org/wiki/Bessel_function http://mathworld.wolfram.com/BesselDifferentialEquation.html use power series method to find it's solution

20. robtobey Group Title

Even though I'm 78 years old and cannot integrate x with pencil and paper, I've access to the computer program, Mathematica 8 Home Editon. that can. The attachment shows the general solution with two constants of integration. A plot of the solution from x = 0 through x = 6 Pi is included.