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Math Help - Differential equation

  1. #1
    Newbie
    Joined
    Feb 2008
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    4

    Exclamation Differential equation

    Help I have no clue how to tackle this question:

    Find the particular solution of:

    dy/dx - 1/x y = x^2 - 3, y(1) = 1/2

    Please can anyone give me some help with this one?

    Any help would be appreciated!!

    Thank you.
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  2. #2
    Super Member
    Joined
    Oct 2007
    From
    London / Cambridge
    Posts
    591
    This is a pretty standard First Order Differential equation.

    the integrating factor is I.F = e^{ \int \frac{-1}{x}}

    I will leave you to simply that.
    then you should know that \frac{d}{dx} \left ( y \cdot I.F \right ) = I.F (x^2-3)

    and the rest should be easy, dont forget your constant for integration.
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