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Math Help - Not understanding this relationship

  1. #1
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    Not understanding this relationship

    The textbook says
    You can verify that the differential equation for the family y= Cx2 can be written as y' = 2y/x
    I think this was stuff in introduction to Diff Q but i don't understand how to look at y= Cx2 and determine it equals y' = 2y/x

    Thank you for all the help
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  2. #2
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    Re: Not understanding this relationship

    Quote Originally Posted by bustacap09 View Post
    The textbook says
    You can verify that the differential equation for the family y= Cx2 can be written as y' = 2y/x
    I think this was stuff in introduction to Diff Q but i don't understand how to look at y= Cx2 and determine it equals y' = 2y/x

    Thank you for all the help
    \displaystyle \begin{align*} y = Cx^2 \end{align*}, so \displaystyle \begin{align*} \frac{2y}{x} = \frac{2\left( Cx^2 \right)}{x} = 2Cx \end{align*}.

    Now differentiating \displaystyle \begin{align*} y = Cx^2 \end{align*} we find \displaystyle \begin{align*} y' = 2Cx \end{align*}, which we have already shown is equal to \displaystyle \begin{align*} \frac{2y}{x} \end{align*}.
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  3. #3
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    Re: Not understanding this relationship

    Thank you
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