Programming help non linear patterns

[euclude]

I want to plot numerically and analytically in order to compare the linear density of bosonic atoms and the chemical potential in function of the non linear dissipation (φ) given by the relation

N(φ)=(αγ+∆)/(βsin⁡(φ))
u(φ)=E+{(αγ+∆)/(tan⁡(φ))}

where a=0.1, γ=0.641, Δ=0.0, φ=3.055

β=∫|ψ|^4dx with 0≤x≤pi and
ψ are eigenfunctions up to order 2 of the mathieu equation given by {(-d^2ψ/dx^2)-kcos(2x)}=Eψ with k=3.0
and E are the eigen values of the same mathieu equation up to order 2.

thank you for your help

 

[NateD]

.To plot the linear density of bosonic atoms and the chemical potential in function of the nonlinear dissipation (φ), given by the equations N(φ)=(αγ+∆)/(βsin⁡(φ)) and u(φ)=E+{(αγ+∆)/(tan⁡(φ))}, with a=0.1, γ=0.641, Δ=0.0, and φ=3.055, you will need to calculate the integrals in the equation for β and numerically solve the Mathieu equation for the eigenvalues E. Once you have those values, you can plot N(φ) and u(φ) on a graph and compare the analytical and numerical solutions.