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Math Help - Integral of inhomogenous dif equation

  1. #1
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    Integral of inhomogenous dif equation

    Hi all

    Can someone please help me find the solution to this question please?
    Attached Thumbnails Attached Thumbnails Integral of inhomogenous dif equation-111.jpg  
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  2. #2
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    Quote Originally Posted by moolimanj View Post
    Hi all

    Can someone please help me find the solution to this question please?
    There's a standard process to follow. Where in this process are you stuck?
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  3. #3
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    Its the x^2 term thats causing me grief.

    Is the solution still of the form: y=p1x+p0
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  4. #4
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    Quote Originally Posted by moolimanj View Post
    Its the x^2 term thats causing me grief.

    Is the solution still of the form: y=p1x+p0
    You try to get a particular solution of the form y = p_2 x^2 + p_1 x + p_0 where the values of p_2 \,, p_1\, and p_0 \, have to be found.

    Substitute the particular solution into the DE:

    5 (2 p_2) + 4(2 p_2 x + p_1) + (p_2 x^2 + p_1 x + p_0) = x^2

    \Rightarrow p_2 x^2 + x(8p_2 + p_1) + (10p_2 + 4p_1 + p_0) = x^2

    Equate coefficients of powers of x:

    p_2 = 1 .... (1)

    8p_2 + p_1 = 0 .... (2)

    10p_2 + 4p_1 + p_0 = 0 .... (3)

    So a particular solution is y = x^2 - 8x + 22.

    Now add this particular solution to the homogenous solution to get the general solution.
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