1. 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

2. Re: Not understanding this relationship

Originally Posted by bustacap09
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*}.

Thank you