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Math Help - help plz!

  1. #1
    Newbie
    Joined
    Jun 2009
    Posts
    8

    help plz!

    I been working on this forever. I am stuck at the integration part.
    the problem is:

    cosysint dy/dt = sinycost

    the answer is
    y=arcsin(C sint)

    Here is my attempt :
    cosy/siny dy = cost/sint dt

    arctany dy = arctant dt

    then i integrate both side and get

    yarctany-1/2ln(1+y^2)=tarctant-1/2ln(1+t^2)

    some there i am stuck.. i dunno how to get the answer y=arcsin(c sint)
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  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
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    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    The D.E. is...

    \cot y\cdot dy = \cot t\cdot dt

    Taking into account that is...

    \int \cot t\cdot dt = \ln \sin t + \ln c

    ... we can separate variables and integrate, so that we obtain...

     \ln \sin y = \ln \sin t + \ln c \rightarrow \sin y = c\cdot \sin t \rightarrow y = \sin ^{-1} (c\cdot \sin t)

    Kind regards

    \chi \sigma
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  3. #3
    Newbie
    Joined
    Jun 2009
    Posts
    8
    thanks alot...
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