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Math Help - Diffy Q

  1. #1
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    Diffy Q

    A function y = g(x) is described by some geometric property of its graph. Write a differential equation of the form dy/dx = f(x, y) having the function g as its solution (or as one of its solutions).

    "The line tangent to the graph of g at the point (x, y) intersects the x-axis at the point (x/2, 0)."
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  2. #2
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    Hi

    The equation of the line tangent to the graph of g at the point whose abscissa is x_0 is y = g'(x_0)(x-x_0)+g(x_0)

    This line intersects the x-axis at the abscissa given by the equation 0 = g'(x_0)(x-x_0)+g(x_0) or x = x_0 - \frac{g(x_0)}{g'(x_0)}

    We know that this abscissa is \frac{x_0}{2} therefore for every x_0 inside g domain

    \frac{x_0}{2} = x_0 - \frac{g(x_0)}{g'(x_0)}

    g'(x_0) = \frac{2\: g(x_0)}{x_0}

    g satisfies the differential equation y' = \frac{2\: y}{x}
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  3. #3
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    thank you much
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