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Math Help - Particular soln of Diff EQ

  1. #1
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    Particular soln of Diff EQ

    The eqn is :

    y" +y' +y = (sin(x))^2

    and i'm in need of a particular solution, y(p).

    I tried y= B/2 - A/2cos(2x)(below)

    y = B/2 - A/2cos(2x)
    y' = Asin(2x)
    y'' = 2Acos(2x)

    Next,

    y" +y' +y = (sin(x))^2

    2Acos(2x)+Asin(2x)+ B/2 - A/2cos(2x) = (sin(x))^2

    I can't anywhere with this.

    The given answer is y(p) = 1/26(13+3cos(2x) -2sin(2x))


    best,
    jblorien
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, jblorien!

    The eqn is: . y'' +y' +y \;= \;\sin^2\!x \;=\;\frac{1}{2} - \frac{1}{2}\cos2x

    and i'm in need of a particular solution, y_p.

    Try: . y_p \;=\;A + B\sin2x + C\cos2x

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  3. #3
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    Thanks a LOT!
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