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Math Help - Differential equation for straight lines through origin

  1. #1
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    Differential equation for straight lines through origin

    Sketch a few members of the straight lines through the origin. By eliminating parameters, derive a differential equation which describes this family.

    Attempt

    y = mx (since there are infinite gradients)

    \frac{dy}{dx} = m

    but the correct answer was: \frac{dy}{dx} = \frac{y}{x}. I am not sure why.
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  2. #2
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    Well, your answer "dy/dx= m" isn't correct because you have not eliminated the parameter m!

    From the original equation, y= mx, m= y/x which gives dy/dx= y/x.
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    Thanks. If instead the question was: find the differential equation for the straight lines through the point (2,3), what would the procedure be?

    I tried using:

    y = mx + c
    3 = 2m + c

    but differentiating it obviously wouldnt work, since there are only constants
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  4. #4
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    Quote Originally Posted by SyNtHeSiS View Post
    Thanks. If instead the question was: find the differential equation for the straight lines through the point (2,3), what would the procedure be?

    I tried using:

    y = mx + c .... (1)
    3 = 2m + c .... (2)

    but differentiating it obviously wouldnt work, since there are only constants
    I have numbered the equations. Solve for c in terms of m from (2). Substitute this expression for c into (1). Now answer the question.
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