solving a 2 point boundary value problem of second order differential equation with variable coefficients

[namrata manglani]

hello ,
i am looking for obtaining a code which can do the following

given : 2nd order differential equation with a variable coefficient k
(simplest example y''+k**2 y=0)

given: 2 boundary values (eg y(0)=0 and y(2pi)=0)

given :o to 2pi int  y*y dx=1 (nomalisation condition

to find : the minimum value of k for which my solution exist in the entire interval.
is there any such code ?

i have tried to have a solution of my differential  equation in terms of k which is trivial using sympy
but m not able to add these conditions to land upto final solution . can anyone help ?

i have tried to write a simple code for the above example which gets stuck the moment i try to add the boundary condition ? anyone has any clue why this is happening.

thank you
regards,
namrata