- #1

Sakha

- 297

- 0

## Homework Statement

[tex]2XY = Y^2 prove that y''2 = \frac{y^{2}-2xy}{(y-x)^3}[/tex]

EDIT: Sorry, don't know how to insert a space in Latex.

## Homework Equations

## The Attempt at a Solution

[tex] 2y+2x \frac{dy}{dx} = 2y \frac{dy}{dx} [/tex]

[tex] \frac{dy}{dx}(2y-2x) = 2y[/tex]

[tex]\frac{dy}{dx}= \frac{y}{y-x} [/tex]

[tex]\frac{d^2y}{dx^2}=\frac{\frac{dy}{dx}(y-x)-(\frac{dy}{dx}-1)y}{(y-x)^2} [/tex]

[tex]\frac{d^2y}{dx^2}= \frac{y^2}{(y-x)^3}[/tex]Is my work correct? If yes, then the question itself is wrong.

In the original equation (2XY = Y

^{2}) does it matters that the letters are caps?