Not understanding this relationship

**bustacap09** · September 13th 2012, 07:03 PM

The textbook says
You can verify that the differential equation for the family y= Cx²can 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= Cx²and determine it equals y' = 2y/x

Thank you for all the help

**Prove It** · September 13th 2012, 07:11 PM

Originally Posted by bustacap09

The textbook says
You can verify that the differential equation for the family y= Cx²can 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= Cx²and 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 $\displaystyle \begin{align*} \frac{2y}{x} \end{align*}$ .

**bustacap09** · September 13th 2012, 07:15 PM

Thank you

Thread: Not understanding this relationship

LinkBack

Thread Tools

Display

Not understanding this relationship

Re: Not understanding this relationship

Re: Not understanding this relationship

Similar Math Help Forum Discussions

Problem in understanding the relationship between concave and quasi-concave function.

relationship help

Relationship between f's

Relationship between ln2, ln3, ln6

Relationship between X and Y!

Search Tags