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Math Help - Quick Differential equation question

  1. #1
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    Quick Differential equation question

    Heys I was wondering if anyone could guide me through this question:
    Let a be a real number. Find the general solution of the differential equation.
    y''' + y'' = a
    Thanks
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Quick Differential equation question

    Quote Originally Posted by Dragonkiller View Post
    Heys I was wondering if anyone could guide me through this question:
    Let a be a real number. Find the general solution of the differential equation.
    y''' + y'' = a
    Thanks
    The characteristic equation will be
    m^3 + m^2 = 0

    m^2(m + 1) = 0

    Two zeros at 0, and one at -1.

    Can you finish from here?

    -Dan
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  3. #3
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    Re: Quick Differential equation question

    Where do I go after finding the homogeneous solution?
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Quick Differential equation question

    You could then assume a particular solution of the form:

    y_p(x)=x^s(A)

    Where the natural number s is chosen to be the smallest value so that no term in the particular solution is a solution to the corresponding homogeneous equation. Hence, let:

    y_p(x)=Ax^2

    and use the method of undetermined coefficients to determine A.
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