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Math Help - Particular Solution to Differential Equation!!!

  1. #1
    Junior Member
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    Particular Solution to Differential Equation!!!

    Hi, I am having trouble trying to figure out the last part. Given the initial conditions, I need to find a solution to the equation.



    Problem:


    Consider the differential equation
    (where primes indicate derivatives with respect to x). Find a particular solution to the differential equation having the form
    using the method of Variation of Parameters. In this, (Note that this asks for and , not and !)
    e^(-4x)

    e^(3x)

    -1

    e^(-7x)


    I am find upto this point.



    TROUBLE WITH THE FOLLOWING PART:


    Then use your solution to find a solution to the differential equation that satisfies the initial conditions , .



    This is where I am stuck. The solution is not right...


    Please help me out,
    Thanks
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  2. #2
    MHF Contributor Calculus26's Avatar
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    the answer should be

    -x^e(-4x) -1/7e^(-4x)+1/7 e^(3x)

    u1 ' = -1 u1 = -x +A

    u2 ' = e^(-7x) u2 = -1/7e^(-7x) + B


    y = -xe^(-4x) - 1/7 e^(-7x) + A e^(-4x) + B e^(3x)

    Applying IC A + B = 1/7

    -4A + 3B = 3/7


    Multiply the top by 4 and add to the bottom you get B = 1/7, A = 0

    -x^e(-4x) -1/7e^(-4x)+1/7 e^(3x) follows
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  3. #3
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    Thanks!!!

    Thanks very much!!!
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