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Math Help - Diffrential Equations..

  1. #1
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    Diffrential Equations..

    The set of solutions of the initial - value problem:




    for x=0, when y=1 satisfy the equation :


    choose one answer:




    I try to solve this question,but I feel my solution is false ..



    ================================================

    Question 2

    The particular solution of differential equation dy/dt=sin 3t

    such that y=-1 at pi/3



    I select the first answer and this is my solution ..




    ================================================

    Question 3
    Solve the differential equation:dy/dx=f(x)
    f(x)=16-x^2
    subject to the condition y(3)=0


    My solution:





    Last edited by change_for_better; May 2nd 2009 at 12:33 PM.
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  2. #2
    Super Member redsoxfan325's Avatar
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    I'm going to look at the first question first.

    \frac{dx}{dy} = e^{y-x} = \frac{e^y}{e^x} \implies e^x\,dx = e^y\,dy

    Integrate and get e^x = e^y+C

    If (0,1) is satisfied, we have 1 = e+C \implies C=1-e.

    So we have e^x=e^y+1-e \implies \boxed{e^x-e^y+e-1=0}

    The other two look fine.
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  3. #3
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    Quote Originally Posted by redsoxfan325 View Post
    I'm going to look at the first question first.

    \frac{dx}{dy} = e^{y-x} = \frac{e^y}{e^x} \implies e^x\,dx = e^y\,dy

    Integrate and get e^x = e^y+C

    If (0,1) is satisfied, we have 1 = e+C \implies C=1-e.

    So we have e^x=e^y+1-e \implies \boxed{e^x-e^y+e-1=0}

    The other two look fine.


    Thank you very much for helping me
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  4. #4
    Super Member redsoxfan325's Avatar
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    You're welcome.
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  5. #5
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    I want to ask you about the following question:




    I try to solve the question but the answer is totally diffrent from the choises

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  6. #6
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    What is The particular solution of differential equation dy/dt=sin 2t such that

    y=3/2 at pi/2


    Can you tell me if my solution true??

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  7. #7
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by change_for_better View Post
    I want to ask you about the following question:




    I try to solve the question but the answer is totally diffrent from the choises

    You're fine through this step: \ln(e^c)=\ln(3) \implies c=\ln(3)

    But \ln(3)\neq 1.

    So you should have y=e^{-2x+\ln(3)} = e^{-2x}\cdot e^{\ln(3)} = \boxed{3e^{-2x}}
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  8. #8
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by change_for_better View Post
    What is The particular solution of differential equation dy/dt=sin 2t such that

    y=3/2 at pi/2


    Can you tell me if my solution true??

    This is correct.
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  9. #9
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    Thank you very much redsoxfan325

    I know my mistake now,

    I calculate ln3 by calculator and the answerwill be 1.09

    so this is my mistake ..
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