I need to solve this differential equation with precise BC:
u′′(x)=ζ−ξ^2*u(x)
u(a)=v1
u′(a)=v1sech(χ⋅a)sinh(χ⋅a)
The solution of this problem provide the slip function u(x) in a mode - 2 Fracture mechanics approach analytical model to investigate bond behaviour in composite materials systems.
However, after many tries I still haven't found a close form solution of the function.
Can anyone help me?
Many thanks in advance