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Math Help - 1st order homogeneous D.E.

  1. #1
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    1st order homogeneous D.E.

    (x+y)\frac{dy}{dx}=x-y
    both homogeneous of degree 0, and I need to use the subs: y=vx dy=vdx+xdv, but I get stuck what exactly to do.

    I got it down to this: x(1-v)dx-x(1+v)vdx+xdv=0 maybe im not seeing something, not exactly sure.
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  2. #2
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    hi I think...
    v= \frac {y}{x}

    \frac {dy}{dx} = v + \frac {dv}{dx}.x


    \frac {dy}{dx} = \frac {1 -v}{1+v}

    ->   v+ \frac {dv}{dx}.x = \frac {1-v}{1+v}


    put v to the other side now we have seprable form
    Last edited by whitepenguin; January 31st 2010 at 05:34 PM.
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  3. #3
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    not quite seeing where you are putting that into...sry
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  4. #4
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    Hi,
       v+ \frac {dv}{dx}.x = \frac {1-v}{1+v}

    \frac{dv}{dx}.x = \frac {1-v}{1+v} -v

    \frac {dv}{dx}.x = \frac {1-v - v(1+v)}{1+v}

    \frac {(1+v)dv}{1-v - v -v^2} = \frac {dx}{x}
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