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Math Help - 2nd order differential

  1. #1
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    2nd order differential

    what do i set y= to to solve this?

    y'' + 4y=sin2x

    ive tried y=asin2x + bcos2x and not had much luck. help please
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  2. #2
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    Hello, sheep99!

    What do i set y= to to solve this?

    . . . y'' + 4y \:=\:\sin2x

    i've tried: y \:=\:A\sin2x + B\cos2x . . . and not had much luck.

    Of course not!

    y \:=\:A\cos2x + B\cos2x is a solution of the homogeneous equation.


    You must try: . y \;=\;Ax\cos2x + Bx\sin2x


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    I came up with: . y_p \;=\;-\tfrac{1}{4}x\cos2x

    The complete solution is: . y \;=\;C_1\cos2x + C_2\sin2x - \tfrac{1}{4}x\cos2x

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