Solving a Complex Second-Degree Ode with Bessel Functions | MATLAB Help

[bloodlines]

Hi friends,

I have been trying to solve the ode of second degree below:

d2y/dz2=(i/a*z+b)*y

i is the complex i, a and b are constants

i ended up with the summation of bessel functions of first end second kind. Then I checked with MATLAB ode solver it gives no explicit solution. please help me.

Thank you so much!

 

[HallsofIvy]

First, your problem is not well written. 1/a*z+b could be interpreted as (1/a)z+ b, or as [1/(az)]+ b, or as 1/(az+ b).

 

[bloodlines]

sorry about that

it is:

d2y/dz2=i*y/(a*z+b)

i is complex i not a symbol

i am also looking for a solution for this wrt z:

d2y/dz2=i*y/(a*z^3+b*z^2+c*z+d)

thank you!

 

[TylerH]

You can get the solution at Wolfram Alpha. http://www.wolframalpha.com/input/?i=d^2y/dx^2=i*y/(a*x+b)

Sorry, but I have no idea as to how you would do it, though.

 

[bloodlines]

thank you so much. i hope i can find a solution to the equation with 3rd degree polynomial.