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Math Help - Calculus problem

  1. #1
    Newbie
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    Calculus problem

    1)  y^3 -y = 2x
    show,
    9(x^2 - \frac{1}{27})\frac{d^2 y}{dx^2} + 9x\frac{dy}{dx}=y

    i tried this few times but i couldn't get the answer


    2)
    \int_0^\pi \frac{x}{1-sin(x)cos(\alpha)}dx= \frac{\pi(\pi -\alpha)}{sin(\alpha)}

    with substitution and using \int_0^a f(x) =\int_0^a f(a-x)
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    first one quite straightforward so i think you should show us some progress.

    as for the second, just put x\longrightarrow\pi-x and your integral becomes \int_{0}^{\pi }{\frac{\pi -x}{1-\sin (x)\cos (\alpha) }}, thus it remains to compute \int_{0}^{\pi }{\frac{dx}{1-\sin (x)\cos (\alpha) }} which shouldn't be that tough.
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  3. #3
    Master Of Puppets
    pickslides's Avatar
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    hi there

    I had a look at question 1

    Using implicit differenitation I found the following

    \frac{dy}{dx} = \frac{2}{3y^2-1}

    \frac{d^2y}{dx^2} = \frac{-24}{(3y^2-1)^3}

    and x = \frac{1}{2}(y^3-y)

    Try to sub these values into the LHS side of the DE and simplyfy, hopefully you will get y.
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