issue with solving system of odes in matlab

syms l g t A omg k

syms f1(x) f2(x)

S = dsolve(diff(f1) == l*f1 + sqrt(g)*A*exp(i*omg*t-i*k*x)*f2, diff(f2) == -sqrt(g)*A*exp(-i*omg*t+i*k*x)*f1 -l*f2)

S.f1

S.f2

matlab shows error when i solve the above mentioned ode in matlab, is there anyone who can guide me to remove the error.

Answer 1

[Walter Roberson]

MATLAB is not powerful enough to solve that analytically. Maple says that the solution is

f1(x) = -(1/2)*exp(1i*omg*t)*(C2*(1i*k-(-k^2-4*A^2*g+(4i)*k*l+4*l^2)^(1/2)+2*l)*exp((1/2)*(1i*k-(-k^2-4*A^2*g+(4i)*k*l+4*l^2)^(1/2))*x)+C1*exp((1/2)*(1i*k+(-k^2-4*A^2*g+(4i)*k*l+4*l^2)^(1/2))*x)*(1i*k+(-k^2-4*A^2*g+(4i)*k*l+4*l^2)^(1/2)+2*l))/(g^(1/2)*exp(i*k*x)*A)

 f2(x) = C1*exp((1/2)*(1i*k+(-k^2-4*A^2*g+(4*1i)*k*l+4*l^2)^(1/2))*x)+C2*exp((1/2)*(1i*k-(-k^2-4*A^2*g+(4*1i)*k*l+4*l^2)^(1/2))*x)

Here, C1 and C2 are arbitrary constants of integration that depend upon the boundary conditions.

[Wajahat]

@Roberson, can you provide me the code of the above solution

[Walter Roberson]

simplify( dsolve([diff(f1(x), x) = l*f1(x)+A*g^(1/2)*exp(-I*k*x+I*omg*t)*f2(x), diff(f2(x), x) = -l*f2(x)-A*g^(1/2)*exp(I*k*x-I*omg*t)*f1(x)]), size)

This is Maple code, not MATLAB code.