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Write 2nd order ODE as system of two 1st order ODEs

  1. Aug 2, 2017 #1

    s3a

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    1. The problem statement, all variables and given/known data
    Write the following second-order ODE as a system of two first-order ODEs.

    ##d^2y/dt^2 + 5(dy/dt)^2 - 6y + e^{sin(t)} = 0##

    2. Relevant equations
    w = dy/dt

    3. The attempt at a solution
    The solution of the book says ##dy/dt = w, dw/dt = -5w - 6y + e^{sin(t)}##, but shouldn't it be ##w = dy/dt, dw/dt = -5w^2 + 6y - e^{sin(t)}##, or am I missing something?
     
  2. jcsd
  3. Aug 2, 2017 #2
    I think you are missing the correct solution manual because I came to the same answer that you did ¯\_(ツ)_/¯
     
  4. Aug 2, 2017 #3

    s3a

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    Lol, great. :P

    Thanks!
     
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