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DiffEQ: Determining the largest interval of a solution

  1. Apr 11, 2009 #1
    The question is to determine the solution to the following 1st order linear DE, along with the largest interval the solution is valid on:

    [tex] cosx \frac{dy}{dx} + (sinx)y=1 [/tex]

    Rewriting it shows it to be linear:
    [tex]\frac{dy}{dx} + (tanx)y = secx[/tex]

    The intergrating factor is: [tex]e^{\int{tanx dx}} = e^{-ln|cosx|} = secx[/tex]

    Multiplying both sides of the DE by the integrating factor, and rewriting the LHS as a derivative of the product of the integrating factor and y:
    [tex]\frac{d}{dx}[(secx)y]= sex^{2}x[/tex]

    (secx)y = tanx+c

    y = sinx + c(cosx)


    Now how do I determine the interval?
  2. jcsd
  3. Apr 11, 2009 #2
    I'm multiplying both sides of the equation by secx, which has a domain of (-pi/2, pi/2), so that's the interval. Is this reasoning correct?
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