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Math Help - sketch an approximation solution

  1. #1
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    sketch an approximation solution

    ok so y(dy/dx) = -x y(0) = 0 and im supposed to draw an approximation solution curve going through the point ? im not sure what i should be doing here. so i separated the variables and got y= sqrt(-x^2 + C). which i dont think can be sketch because its negative under the radical sign. any help would be appreciated
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  2. #2
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    \displaystyle y\,\frac{dy}{dx} = -x

    \displaystyle \int{y\,\frac{dy}{dx}\,dx} = \int{-x\,dx}

    \displaystyle \int{y\,dy} = -\frac{x^2}{2} + C_1

    \displaystyle \frac{y^2}{2}+C_2 = -\frac{x^2}{2} + C_1

    \displaystyle \frac{y^2}{2} = -\frac{x^2}{2} + C_1 - C_2

    \displaystyle y^2 = -x^2 + C where \displaystyle C = 2C_1 - 2C_2

    \displaystyle x^2 + y^2 = C.


    Once you use your initial condition to find \displaystyle C = 0, you'll see that this is a circle of radius \displaystyle 0, in other words, the only point is the origin.
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  3. #3
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    thanks. let me go back and re work it.
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