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Math Help - Differential Equations

  1. #1
    Senior Member mollymcf2009's Avatar
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    Differential Equations

    **PLEASE don't solve this, I just want to know if my process is correct. Thanks!

    Which of the following functions are solutions of the differential equation:

    y'' + y = sin(x)?

    a) y = sin(x)

    b) y = xsin(x) - 8xcos(x)

    c) y = -\frac{1}{2}xcos(x)

    d) y = cos(x)

    e) y = \frac{1}{2}xsin(x)

    Just want to make sure I'm doing this correctly.

    First, I get y'' of each of these. Plug y'' & y into the DE and simplify without moving anything to different sides of the equation. Then if whatever is on the left ends up = sin(x) then it IS a solution. Is this the right way to do this?
    Thanks!
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  2. #2
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    skeeter's Avatar
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    Quote Originally Posted by mollymcf2009 View Post
    **PLEASE don't solve this, I just want to know if my process is correct. Thanks!

    Which of the following functions are solutions of the differential equation:

    y'' + y = sin(x)?

    a) y = sin(x)

    b) y = xsin(x) - 8xcos(x)

    c) y = -\frac{1}{2}xcos(x)

    d) y = cos(x)

    e) y = \frac{1}{2}xsin(x)

    Just want to make sure I'm doing this correctly.

    First, I get y'' of each of these. Plug y'' & y into the DE and simplify without moving anything to different sides of the equation. Then if whatever is on the left ends up = sin(x) then it IS a solution. Is this the right way to do this?
    Thanks!
    yes
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