# issue with solving system of odes in matlab

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Wajahat am 5 Okt. 2017
Kommentiert: Walter Roberson am 24 Jan. 2018
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.
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### Akzeptierte Antwort

Walter Roberson am 5 Okt. 2017
Bearbeitet: Walter Roberson am 24 Jan. 2018
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.
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Walter Roberson am 24 Jan. 2018
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.

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