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Math Help - General solution question

  1. #1
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    General solution question

    Find the solution of y'' + 25y = 150cos(5t)

    I have found the the complimentary function to be y= Acos(5t) + Bsin(5t)

    When I worked out the particular integral I came as far as this:

    t(-25C cos(5t) - 25Dsin(5t)) - 10Csin(5t) + 10Dcos(5t) + 25t(Ccos(5t) + Dsin(5t)) = 150 cos (5t)

    What i dont unerstand is why the above simpifies to 150cos(5t)??

    Thank you for any help.
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  2. #2
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    You'll notice the first group of terms cancel with the last group leaving

    -10C\sin(5t) + 10D\cos(5t) = 150 \cos (5t)

    SO, can you choose C and D so that the left side = the right side?
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  3. #3
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    yeah it makes sense. I worked out d=15 and c=0. hence yp= 15tsin(5t)
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by alpha View Post
    Find the solution of y'' + 25y = 150cos(5t)

    I have found the the complimentary function to be y= Acos(5t) + Bsin(5t)

    When I worked out the particular integral I came as far as this:

    t(-25C cos(5t) - 25Dsin(5t)) - 10Csin(5t) + 10Dcos(5t) + 25t(Ccos(5t) + Dsin(5t)) = 150 cos (5t)

    What i dont unerstand is why the above simpifies to 150cos(5t)??

    Thank you for any help.
    If you have a table of Laplace transforms available you can do this by taking the LT of the ODE with initial conditions y(0)=y'(0)=0, Simplify and rearrange and look up what the result is the LT of.

    CB
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