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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

    Mark44

    Staff: Mentor

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

    cronxeh

    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)

    y(x)=(x^10+89)/(5x^7)
     
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