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Homework Help: 1st order linear differential eq. using integrating factor

  1. Jun 3, 2010 #1
    1. The problem statement, all variables and given/known data
    Solve the inital value problem for y(x); xy′ + 7y = 2x^3 with the initial condition: y(1) = 18.
    y(x) = ?

    2. Relevant equations
    dy/dx +P(x)y=Q(x), integrating factor=e^∫P(x) dx

    3. The attempt at a solution
    Multiplied all terms by 1/x to get it in correct form dy/dx+7y/x=2x^2
    integrating factor=e^∫7/x dx=x^7
    here is where i get lost do i multiply everything back into the original eq. or am i already off. I am not getting the correct answer.
  2. jcsd
  3. Jun 3, 2010 #2
    Maybe it's just a typo, but you might want to revise your integrating factor.
  4. Jun 3, 2010 #3


    Staff: Mentor

    [tex]\int \frac{7 dx}{x} \neq x^7[/tex]
  5. Jun 3, 2010 #4


    User Avatar
    Gold Member

    Once you get the correct integrating factor M(x) you will multiply it out over entire equation, on both sides. Your equation will then reduce to y(x)M(x)=Integral(M(x)Q(x)dx) + C. to get y(x) you will integrate and plug in the initial conditions.

    y(x) = (Integral(M(x)Q(x)dx) + C) / M(x)

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