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Math Help - check my work please (difEq)

  1. #1
    Member pberardi's Avatar
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    check my work please (difEq)

    Solve: x*cot(y) = dy/dx*sec(x) = 0

    -dy/dx*sec(x) = -x*cot(y)
    dy/dx*sec(x) = x*cot(y)
    dy/cot(y) = x*dx/(sec(x))
    integration
    -ln|cos(y)| = x*sin(x) + cos(x) + C
    ln|cos(y)| = -x*sin(x) - cos(x) + A
    cos(y) = e^(-x*sin(x) - cos(x) + A)
    y = arccos(e^(-x*sin(x) - cos(x))+ A

    Is it correct and can I write this better? Thanks.
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Quote Originally Posted by pberardi View Post
    Solve: x*cot(y) = dy/dx*sec(x) = 0

    -dy/dx*sec(x) = -x*cot(y)
    dy/dx*sec(x) = x*cot(y)
    dy/cot(y) = x*dx/(sec(x))
    integration
    -ln|cos(y)| = x*sin(x) + cos(x) + C
    ln|cos(y)| = -x*sin(x) - cos(x) + A
    cos(y) = e^(-x*sin(x) - cos(x) + A)
    y = arccos(e^(-x*sin(x) - cos(x))+ A ... not +A

    e^{-x*sin(x) - cos(x) + A} = e^{-x*sin(x) - cos(x)} \cdot e^{A}

    y = \arccos[Be^{-x\sin{x}-\cos{x}}]

    Is it correct and can I write this better? Thanks.
    ok?
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