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First Order Linear Differential Equation

  1. Feb 23, 2009 #1
    1. The problem statement, all variables and given/known data
    10 y′+ 10 y = 7 exp(6*x)
    y ( 0 ) = 7



    2. Relevant equations



    3. The attempt at a solution

    First I divided everything by 10 because the coefficient of the y' should be 1
    Then I found the integrating factor, which was exp(integral of 1*dx) = exp(x) = Integrating factor

    I multiplied to all three terms:
    exp(x)*y' + exp(x)*y = (7*exp(2x))/10
    (y*exp(x))' = (7*exp(2x))/10

    I then integrated the above and got
    y*exp(x) = exp(7x)/10 + C
    y = exp(6x)/10 + C

    Solving for c y ( 0 ) = 7

    7 = exp(0)/10 + C
    7 = 1/10 + C
    C = 69/10

    I got my final answer to be y = (exp(6x)+69)/10

    However, the my homework says thats wrong. Does anyone know where I messed up?

    Thanks
     
  2. jcsd
  3. Feb 23, 2009 #2

    djeitnstine

    User Avatar
    Gold Member

    Your algebra is off, because when you divide the right side you should get y=exp(6x)/10 + C*exp(-x)
     
  4. Feb 23, 2009 #3
    I just realized that too. Thank you
     
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