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Math Help - Introduction to Systems of Differential Equations: The Method of Elimination

  1. #1
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    Introduction to Systems of Differential Equations: The Method of Elimination

    Please Help mewith this problem, I am not really getting the double prime stuff...

    -Find the General Solution to the system

    { x'' = -5x + 2y
    { y'' = 2x - 8y
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  2. #2
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    Quote Originally Posted by googoogaga View Post
    Please Help mewith this problem, I am not really getting the double prime stuff...

    -Find the General Solution to the system

    { x'' = -5x + 2y
    { y'' = 2x - 8y
    2y = x''+5x\implies 2y''=x''''+5x''
    Substitute,
    x''''+5x'' = 4x - 8x'' - 40x
    x'''' + 13 x'' +40 x = 0
     x = C_1\sin (t\sqrt{5})+C_2\cos (t\sqrt{5})+C_3\sin (t\sqrt{8})+C_4\cos (t\sqrt{8})

    You do now "y".
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