Solving a Sturm Liouville Problem: d/dx(sinx . dy/dx)+(8 sinx - 12 sin3x - m . sinx )

[Negar]

Hello,

I am working on a analytical model, and I need to solve two Sturm Liouville equations. The first one is as follows:

d/dx(sinx . dy/dx)+(8 sinx - 12 sin³x - m . sinx )y=0 ( m is the eigenvalue)

at x=0 dy/dx=0;

at x= pi/2 y=0;

(nonhomogeneous equation and homogeneous BCs.)

I really appreciate it if anybody can help me to solve his equation.

 

[Deleted member 4993]

Hello,

I am working on a analytical model, and I need to solve two Sturm Liouville equations. The first one is as follows:

d/dx(sinx . dy/dx)+(8 sinx - 12 sin³x - m . sinx )y=0 ( m is the eigenvalue)

at x=0 dy/dx=0;

at x= pi/2 y=0;

(nonhomogeneous equation and homogeneous BCs.)

I really appreciate it if anybody can help me to solve his equation.

What type of SL equation is this?

(i)regular Sturm-Liouville Eigen Value Problem (SL-EVP)

(ii) a singular SL-EVP

(iii) a periodic SL-EVP.