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Math Help - Clarification of a DE example

  1. #1
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    Clarification of a DE example

    My book states that:
    y'' +4y = 0
    has a general solution of:
    y(t) = c_1\cos {2t} + c_2\sin{2t}

    I dont see how they achieve this since the initial equation has a characteristic form of:
     r^2 + 4 = 0
     r_{1,2} = \pm 2
     \therefore
    y(t) = c_1e^{2t} + c_2e^{-2t}
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sixstringartist View Post
    My book states that:
    y'' +4y = 0
    has a general solution of:
    y(t) = c_1\cos {2t} + c_2\sin{2t}

    I dont see how they achieve this since the initial equation has a characteristic form of:
     r^2 + 4 = 0
     r_{1,2} = \pm 2
     \therefore
    y(t) = c_1e^{2t} + c_2e^{-2t}
    no, you solutions are not correct, we have complex solutions here. your solutions work for the difference of two squares, you have the sum of two squares here. use the quadratic formula
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  3. #3
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    Thank you. In my haste I was taking the sqrt of 4 and not -4. Thanks again.
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