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Math Help - seperation of variables help

  1. #1
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    Exclamation seperation of variables help



    do i take the ln or do i use partial fractions i dont know how t start it plz help
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  2. #2
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    Quote Originally Posted by bsanghera View Post


    do i take the ln or do i use partial fractions i dont know how t start it plz help
    Separate

     <br />
\frac{dy}{\sqrt{1-y^2}} = \frac{dt}{t}.<br />
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    Exclamation

    [quote=Danny;381710]Separate

     <br />
\frac{dy}{\sqrt{1-y^2}} = \frac{dt}{t}.<br />
[/quote

    lol yess i kniw that much but i was asking what to do aftr that do i take the natural log?
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    [quote=bsanghera;381729]
    Quote Originally Posted by Danny View Post
    Separate

     <br />
\frac{dy}{\sqrt{1-y^2}} = \frac{dt}{t}.<br />
[/quote

    lol yess i kniw that much but i was asking what to do aftr that do i take the natural log?
    So \sin ^{-1} y = \ln t + c = \ln t + \frac{\pi}{2} (from the IC).

    Taking sin's gives

     <br />
y = \sin \left(\ln t + \frac{\pi}{2}\right)<br />
.
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