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Math Help - O D E question

  1. #1
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    O D E question

    Hi there,

    Can anybody show me how to solve an O D E with a square root in it?
    I just don't get it

    y'=\sqrt{4+2y-1}
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Quote Originally Posted by miepie View Post
    Hi there,

    Can anybody show me how to solve an O D E with a square root in it?
    I just don't get it

    y'=\sqrt{4+2y-1}
    \frac{dy}{dx} = \sqrt{3 + 2y}

    \frac{dy}{\sqrt{3+2y}} = dx

    \frac{2}{\sqrt{3+2y}} \, dy = 2 \, dx

    integrate ...
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  3. #3
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    I made a mistake, there is also an x on the right side, that's my greatest problem. This is the good one:

    <br />
y'=\sqrt{4x+2y-1}<br />

    Thanks for helping!
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  4. #4
    Math Engineering Student
    Krizalid's Avatar
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    Put {{u}^{2}}=4x+2y-1\implies 2uu'=4+2y'\implies uu'=2+y', and the ODE becomes \frac{u}{u+2}\,du=dx which after some of integration it's \sqrt{4x+2y-1}-2\ln \left( \sqrt{4x+2y-1}+2 \right)=x+k.
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