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Math Help - Solve y ′′ − 3 y ′ − 4 y = −3 x+5

  1. #1
    Newbie lemonlime's Avatar
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    Solve y ′′ − 3 y ′ − 4 y = −3 x+5

    Solve the differential equation
    y ′′ − 3 y ′ − 4 y = −3 x+5


    I've worked out the independent solution which is
    r^2 - 3r - 4 = 0

    (r + 1) (r - 4)

    {e^(-1*x), e^(4*x)}
    (as a set of function)

    Now my question is how do I find the solution of the original d.e. is of form
    y(x) = u1v1 + u2v2

    And the general solution?
    Last edited by mr fantastic; June 3rd 2010 at 06:15 AM. Reason: Re-titled.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by lemonlime View Post
    Solve the differential equation
    y ′′ − 3 y ′ − 4 y = −3 x+5
    This is a linear constant coefficient ordinary differential equation. The general solution is of the form:

    y(x)=G(x)+p(x)

    where G(x) is the general solution of the homogeneous equation:

     <br />
y''-3y'-4y=0<br />

    (you seem to know how to do this) and p(x) is any particular solution of the full equation. To find a particular solution use a trial solution of the for y(x)=ax+b, plug this into the original equation and find what a and b need to be for the equation to be satisfied.

    CB
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