You have the time derivative of an expression being zero, right? That means the expression does not change with respect to time. Therefore it is constant. It's no different from solving the differential equation If you integrate both sides, you're going to get right? The fact that instead of on the LHS you have doesn't change how you can integrate the DE. Make sense?Firstly, I don't understand how this goes from (2) to (3)...

All they did was differentiate the , cancel all the 2's, and re-arrange. That is:...again, in this example I don't understand how 11 was arrived at from 10.

So there's considerably less there than meets the eye. It's all regular calculus.