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Homework Help: Urgent: Needed for Calculus Exam!

  1. Oct 31, 2004 #1
    Just a question to clear things up regarding to the integrating factors for my exams tomorrow:

    The standard first order differential equation has the form:

    dy/dx + p(x)*y = q(x).

    where the integrating factor is e^(integral of p(x) dx).

    But in one of the previous year paper, it has the equation

    dy/dt + bt = a

    where "b" and "a" are constants. To me, this does not resembles the standard form.

    But apparently it is, in the answer they used the integral factor
    e^(integral of b) and solved the equation.

    I must have missed some important points in how to identify integrating factors...
     
  2. jcsd
  3. Oct 31, 2004 #2

    cepheid

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    It's a special case of the standard from in which p(x) and q(x) are constant functions! So, it's an easier to solve case. But it's still a linear equation, so why wouldn't the method of integrating factors work? The standard form is just the most general case.

    Edit: Why did you post a question about differential equations in the Kindergarten to Grade 12 HW Help forum? :rofl:

    Edit: I didn't read the problem carefully before. Furthermore, it should be even easiser to solve, because p(x) = 0! There is no 'y' term.

    Edit: At third glance, the problem is SO easy, that although it is a linear equation, it doesn't even merit the method of integrating factors! You have dy/dt = q(t). Why not just integrate directly?

    [tex] \frac{dy}{dt} = a - bt [/tex]

    [tex] y = \int{(a-bt)}dt [/tex]

    Right?
     
    Last edited: Oct 31, 2004
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