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Thread: Please help with tricky question

  1. #1
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    Please help with tricky question

    Hey guys so I need some help solving this..

    Verify y=2cosx -cosxsinx

    solves intial value problem y(dash) + (tanx)y = -cos^2x, y(0)=2

    The y dash means the first derivative
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  2. #2
    MHF Contributor
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    Re: Please help with tricky question

    $y=2\cos(x)-\cos(x)\sin(x)$

    $y^\prime = -2\sin(x) - (-\sin^2(x) +\cos^2(x)) = -2\sin(x) - 1+2\sin^2(x)$

    $y^\prime +\tan(x) y = -2\sin(x) - 1+2\sin^2(x) + \tan(x)(2\cos(x)-\cos(x)\sin(x))=$

    Spoiler:
    $-2\sin(x) - 1+2\sin^2(x) + 2\sin(x) - \sin^2(x)=$

    $\sin^2(x) -1=$

    $-\cos^2(x)$

    checking $y(0)$ we get

    Spoiler:
    $y(0) = 2\cdot 1 - 1\cdot 0 = 2$
    Thanks from topsquark
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