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Homework Help: Resulting system of equations is not linearly independent

  1. Apr 16, 2015 #1
    1. The problem statement, all variables and given/known data
    Solve 2x''+3x'+40x = 40y+3y'

    2. Relevant equations
    y = 0.05sin(10t)

    3. The attempt at a solution
    I used the annihilator method to find the answer of x(t) = Acos(10t)+Bsin(10t)+Ce-0.75tcos(sqrt(311)/4t)+De-0.75tsin(sqrt(311)/4t) where A, B, C and D are constants.

    The initial conditions were given as x(0)=0, x'(0)=0, x''(0)=0 and I used 2x''(0)+3x'(0)+40x(0) = 40y(0)+3y'(0) for the last one giving:

    0 = A + C

    0 = 10B - 0.75C + [sqrt(311)/4]D

    0 = 100A +(151/8)C + 3[sqrt(311)/8]D

    -160A+30B = 1.5

    I know these are right because I double checked with matlab so I'm not really sure what's wrong, but as I said the set is not linearly independent.
  2. jcsd
  3. Apr 16, 2015 #2


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    You mean ##Ce^{-\frac 3 4 t}\cos(\frac{\sqrt {311}}{4}t)+De^{-\frac 3 4 t}\sin(\frac{\sqrt {311}}{4}t)## for the complementary solution ##y_c## part of that.

    What isn't linearly independent? The two terms in ##y_c## certainly are.
  4. Apr 16, 2015 #3


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    The given initial conditions are inconsistent. If you plug in the initial conditions on the lefthand side and set t=0 in the righthand side, you get 0 = 3/2.

    The problem is overconstrained as well. If you were to use the method of underdetermined coefficients, you'd only have two undetermined constants, but you have three initial conditions.
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