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Math Help - diff eqn with cos and i?

  1. #1
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    diff eqn with cos and i?

    Here it is...
    d2y/dx2 + 4y=cos(x) , y(0)=1, dy/dx(0)=1. If I am correct, lambda is for this one 2i and -2i. I'm not sure if i'm doing this right... in any case, what do with this cos(x)?

    How to solve this? And what do u get? I'm kinda stuck...
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  2. #2
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    Quote Originally Posted by fiksi View Post
    Here it is...
    d2y/dx2 + 4y=cos(x) , y(0)=1, dy/dx(0)=1. If I am correct, lambda is for this one 2i and -2i. I'm not sure if i'm doing this right... in any case, what do with this cos(x)?

    How to solve this? And what do u get? I'm kinda stuck...
    Yes on 2i, -2i. Your complimentary solution is

    y_c = c_1 \sin 2x + c_2 \cos 2x. It obtain a particualr solution, try a form y_p = A \sin x + B \cos x, sub into the ODE and compare terms. This will give you an A and B. Then use your IC's.
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  3. #3
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    if i get u correctly, trying this...

    i get final solution y=1/3cosx + 1/2sin(2x)+ 2/3 cos(2x). Is that it?
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  4. #4
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    Quote Originally Posted by fiksi View Post
    if i get u correctly, trying this...

    i get final solution y=1/3cosx + 1/2sin(2x)+ 2/3 cos(2x). Is that it?
    Yep
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