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Math Help - write the general solution...

  1. #1
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    write the general solution...

    the eigenvalues for X'=AX as [3-i,3+i,-3] with the eigenvectors of [1,(-5+7i)/2, (5-3i)/2] and [1, (-5-7i)/2, (5+3i)/2 ]

    im supposed to write the general solution using only real coefficients...

    im not sure how to do this problem....

    a little help would be nice..

    thanks in advance
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Use

    e^{(3+i)t}+e^{(3-i)t}=2e^{3t}\cos t

    e^{(3+i)t}-e^{(3-i)t}=2ie^{3t}\sin t
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  3. #3
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    sorry i left out one vector...

    [1,0,-1/3]

    this is what i know about the problem thus far....

    this is what i know so far....

    i know lambda will equal to 3+i

    i also know the formula is X1=C1[B1*cos t - B2*sin t ]e^3t

    X2= C2[B2*cos t + B1*sin t]e^3t...

    X3, im not so sure about....
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    If v_1,v_2,v_3 are the corresponding eigenvectors associated to 3,3+i,3-i respectively, write X=C_1e^{3t}v_1+C_2e^{(3+i)t}v_2+C_3e^{(3-i)t}v_3 and use the equalities of answer #2.
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