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Math Help - [SOLVED] Second order differential equations

  1. #1
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    [SOLVED] Second order differential equations

    b)
    Solve the initial value problem

    y′′ + 2y′ + 5y = 0, y(0) = −2, y′(0) = 2

    and write the final solution using real valued functions.

    I did the question and got the answer to be Y = -2(e^x)cos2(x) is ithis right?

    Help will be appreciated...thank you
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by rajr View Post
    b)
    Solve the initial value problem

    y′′ + 2y′ + 5y = 0, y(0) = −2, y′(0) = 2

    and write the final solution using real valued functions.

    I did the question and got the answer to be Y = -2(e^x)cos2(x) is ithis right?

    Help will be appreciated...thank you

    So the auxillary equation is

    m^2+2m+5=0 \implies (m+1)^2+4=0 \implies m=-1 \pm 2i

    this tells us that our solution is of the form

    y=c_1e^{-x}\cos(2x)+c_2e^{-x}\sin(2x)

    Your answer is correct except for the missing minus sign in you exponential
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