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Thread: (sinx) dy + ( y cosx - x sinx ) =0

  1. #1
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    (sinx) dy + ( y cosx - x sinx ) =0

    the pic post is the solving using exact equation method , but
    the author solve it using another method ( i typed below)

    after rearranging , we have

    dy/dx + y cotx = x


    integrating factor = sin x

    d/dx( ysinx) = ∫x sinx dx

    so , finally , i have ysinx +xcosx - sinx = C

    why not the final ans =
    ysinx +xcosx - sinx + C = 0 ???(sinx) dy + ( y cosx - x sinx ) =0-dsc_0387.jpg(sinx) dy + ( y cosx - x sinx ) =0-dsc_0388.jpg
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  2. #2
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    Re: (sinx) dy + ( y cosx - x sinx ) =0

    $\displaystyle C$ is an arbitrary constant - any value for $\displaystyle C$ is valid. Instead of writing $\displaystyle C$ we might write $\displaystyle C_1=-C$ which is still an arbitrary constant, and then your result comes out exactly.
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