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  1. #1
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    Equation

    A curve which passes through the point (1,0) satisfies the equation dx/dy = x

    Find its equation


    thanks for any help
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  2. #2
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    Hello, gracey!

    A curve which passes through the point (1,0)
    satisfies the equation: . \frac{dx}{dy} \:=\:x^3
    Find its equation
    This is a Differential Equation problem . . .


    We have: . \frac{dy}{dx} \:=\:x^{-3} \quad\Rightarrow\quad dy \:=\:x^{-3}\,dx

    Integrate: . \int dy \;=\;\int x^{-3}\,dx \quad\Rightarrow\quad y \;=\;-\frac{x^{-2}}{2} + C  \;=\;-\frac{1}{2x^2} + C


    Since (1,0) satisfies the equation: . 0 \:=\:-\frac{1}{2\cdot1^2} + C \quad\Rightarrow\quad C \:=\:\frac{1}{2}


    Therefore, the equation is: . y \;=\;-\frac{1}{2x^2} + \frac{1}{2}

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  3. #3
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    Quote Originally Posted by gracey View Post
    A curve which passes through the point (1,0) satisfies the equation dx/dy = x

    Find its equation


    thanks for any help
    \frac{dy}{dx} = x^{-3}.

    Integrate to get y as a function of x. Use "curve which passes through the point (1,0)" to evaluate the constant of integration.
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