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Partial differential equation reduced but

  1. May 14, 2010 #1
    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...
  2. jcsd
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