Solving diffrential equations

Well i couldn't go to school today for various reasons.

So i'm trying to teach myself some stuff and am having trouble understanding the method.

Quote:

Find a differential equation satisfied by y = Ax^2 + Bx^0.5 for ALL values of A and B

The method goes like this :

if

$\displaystyle y = Ax^2 + Bx^0.5$

then

$\displaystyle \frac{dy}{dx} = 2Ax + \frac{1}{2}Bx^0.5$

and $\displaystyle \frac{d^2y}{dx^2} = 2A - \frac{1}{4}Bx^0.5$

Ok, i get that :) and i also get you can use elimination to then solve this...but i don't get what they've done...

By eliminating B from the first and second equation...they get

$\displaystyle y - 2x\frac{dy}{dx} = A(x^2 - 4x^2) + B(x^0.5 - x^0.5) $

This is where im confused...where the hell do they even get $\displaystyle 2x\frac{dy}{dx}$

from?

Note: Its meant to be x to the power of a half...but latex doesnt like it lol.

Thank-you