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Homework Help: Is this general solution for ODE correct?

  1. Mar 23, 2010 #1
    Find the general solution of the following ODE:

    dx/dt = 3x^(2) cos t



    Make x the subject of the solution.



    Heres my solution, is this correct?

    dx/dt = 3x^(2) cos t

    dx/3x^(2) = cos t dt

    Integrating both sides gives:

    ln (3x^(2)) = sin t + C

    3x^(2) = e^(sin t + C)

    3x^(2) = Ae^(sin t)

    x^(2) = (Ae^(sin t))/3)

    x = SQRT(Ae^(sin t))/3)
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 23, 2010 #2

    rock.freak667

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    here is where you went wrong,

    1/3x2 can be written as x-2/3.

    You know that ∫xn dx = xn+1/(n+1) + C for n≠-1
     
  4. Mar 23, 2010 #3
    So from what you have said:

    ∫dx/3x^(2) = -1/3x + C or (-x^(-1)/3) + C

    Giving a solution of:

    -1/3x + C = sin t
     
  5. Mar 23, 2010 #4

    rock.freak667

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    That should be correct.
     
  6. Mar 23, 2010 #5

    vela

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    You can easily check your answer by plugging it back into the original differential equation and seeing if it works.
     
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