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Math Help - differential eqns ( try one please)

  1. #1
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    differential eqns ( try one please)

    -4x+y+(x+4y)y'=0

    give value for k in which differential eqn is exact
    10x^19*y^2+kx^20*y+(x+y)*x^20 dy/dx =0

    dy/dx=2x^2-3x-2+(2/x)*y

    dy/dx=(6-(x+3)y)/x+2
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  2. #2
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    Quote Originally Posted by samdmansam View Post
    -4x+y+(x+4y)y'=0

    give value for k in which differential eqn is exact
    10x^19*y^2+kx^20*y+(x+y)*x^20 dy/dx =0

    dy/dx=2x^2-3x-2+(2/x)*y

    dy/dx=(6-(x+3)y)/x+2

    \frac{dy}{dx}=2x^2-3x-2+\frac{2}{x}y

    \frac{dy}{dx}-\frac{2}{x}y=2x^2-3x+2

    so we need our integration factor

    I(x)=e^{\int \frac{2}{x}dx}=e^{2 \ln(x)}=e^{\ln(x)^2}=x^2

    x^2\frac{dy}{dx}-2xy=2x^4-3x^3-2x \iff \frac{d}{dx}\left[ x^2y \right]= 2x^4-3x^3-2x

    integratin we get

    x^2y=\frac{2}{5}x^5-\frac{3}{4}x^4-x^2+c

    y=\frac{2}{5}x^3-\frac{3}{4}x^2-1+cx^{-2}
    Last edited by TheEmptySet; April 10th 2008 at 10:00 PM.
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