Not understanding this relationship

The textbook says

You can verify that the differential equation for the family y= Cx^{2 }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= Cx^{2 }and determine it equals y' = 2y/x

Thank you for all the help

Re: Not understanding this relationship

Quote:

Originally Posted by

**bustacap09** The textbook says

You can verify that the differential equation for the family y= Cx^{2 }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= Cx^{2 }and determine it equals y' = 2y/x

Thank you for all the help

$\displaystyle \displaystyle \begin{align*} y = Cx^2 \end{align*}$, so $\displaystyle \displaystyle \begin{align*} \frac{2y}{x} = \frac{2\left( Cx^2 \right)}{x} = 2Cx \end{align*}$.

Now differentiating $\displaystyle \displaystyle \begin{align*} y = Cx^2 \end{align*}$ we find $\displaystyle \displaystyle \begin{align*} y' = 2Cx \end{align*}$, which we have already shown is equal to $\displaystyle \displaystyle \begin{align*} \frac{2y}{x} \end{align*}$.

Re: Not understanding this relationship