hi everyone, I have been stuck alot of times on that so please help me , I need to solve coupled differential equation with constraint,

d(c_g)/dt=(i(dc_g)/dt=(i/ℏ)*(E_g+A*cos(wt) )*c_g+B*cos(wt)*c_e

d(c_e)/dt=(i/ℏ)*(E_e+D*cos(wt) )*c_e+C*cos(wt)*c_g

With constrain

 |c_e |^2+|c_g |^2=1
 c_g (t=0)=1
 c_e (t=0)=0

I tried the following code :

syms c_g(t) c_e(t)

ode1 = diff(c_g) == (-1i/hbar)*((E_g+A*perturb(t))*c_g+B*perturb(t)*c_e);

ode2 = diff(c_e) == (-1i/hbar)*((E_fex+D*perturb(t))*c_e+C*perturb(t)*c_g);

odes = [ode1; ode2];

cond1 = c_g(0) == 1;

cond2 = c_e(0) == 0;

conds = [cond1; cond2];

[c_g(t), c_e(t)] = dsolve(odes,conds);

fplot(abs(c_g).^2)

hold on

fplot(abs(c_e).^2)

grid on

legend('c_g^2','c_e^2','Location','best')

so how could I enter the constraint to matlab , c_e^2,c_g^2 are probabilities