Hi everybody... I have problem with this system of equation

d^4 (T1[t])/dt^4 + (A1 - B1*f[x])*d^2 (T1[t])/dt^2 + (C1 + D1*f[x])*
T1[t] - E1*T2[t] = 0

d^4 (T2[t])/dt^4 + (A2 - B2*f[x])*d^2 (T2[t])/dt^2 + (C2 + D2*f[x])*
T2[t] - E2*T1[t] = 0

X[x] = (Ch[k*x] + Cos[k*x])/(Ch[k*l] - Cos[k*l]) - (Sh[k*x] +
Sin[k*x])/(Sh[k*l] - Sin[k*l]);

f[x] = X''[x]/X[x];

A1,B1,C1,D1,E1,A2,B2,C2,D2,E2,l,l are constants. The solutions are in this form e^i*r*t. And than I can get a determinant which must be equal to zero because of non trivial solutions. Form is

r[x]^4-V1[x]*r[x]^2+P1[x] -S1
-S2 r[x]^4-V2[x]*r[x]^2+P2[x]

S1,S2 are constants

I need a solutions r, not a solutions r as a function of x. PLEASE!!!!!!! Ritz method can help but ...

Derdack in big problem...