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Math Help - Proving a conjecture in differentiation

  1. #1
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    Proving a conjecture in differentiation

    How do I prove the conjecture that

    d^(n)y
    ______ = k^(n) y
    dx^(n)


    The n are in the same position like 2 in the second derivative, d2y/dx2. And the n on the RHS is an exponent, but the y is not.

    I know to use induction but I'm stuck at proving P(k+1),

    d^(k+1)y
    ______
    dx^(k+1)

    Thank you very much!
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  2. #2
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    Re: Proving a conjecture in differentiation

    for n = 1

    \frac{dy}{dx} = ky

    assume true for n ...

    \frac{d^ny}{dx^n} = k^n y

    \frac{d}{dx} \left[\frac{d^ny}{dx^n} = k^n y\right] =  \frac{d^{n+1}y}{dx^{n+1}} = k^n \cdot \frac{dy}{dx} = k^n \cdot ky = k^{n+1} y
    Thanks from Tutu
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  3. #3
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    Re: Proving a conjecture in differentiation

    Quote Originally Posted by Tutu View Post
    How do I prove the conjecture that

    d^(n)y
    ______ = k^(n) y
    dx^(n)
    skeeter does this using induction on n and assuming that dy/dx= ky is that true? You do not mention it in your post but without that conclusion is not true.

    The n are in the same position like 2 in the second derivative, d2y/dx2. And the n on the RHS is an exponent, but the y is not.

    I know to use induction but I'm stuck at proving P(k+1),

    d^(k+1)y
    ______
    dx^(k+1)

    Thank you very much!
    Follow Math Help Forum on Facebook and Google+

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