Equation referencing

A few examples of equation referencing by their numbers:

Here is a labeled equation:
$$x+1\over\sqrt{1-x^2}\label{ref1}$$
with a reference to ref1:\eqref{ref1},
and another numbered one with no label:
$$x+1\over\sqrt{1-x^2}$$
This one uses \nonumber:
$$x+1\over\sqrt{1-x^2}\nonumber$$

Here's one using the equation environment:
\begin{equation}
x+1\over\sqrt{1-x^2}
\end{equation}
and one with equation* environment:
\begin{equation*}
x+1\over\sqrt{1-x^2}
\end{equation*}

This is a forward reference [\ref{ref2}] and another \eqref{ref2} for the
following equation:
$$x+1\over\sqrt{1-x^2}\label{ref2}$$
More math:
$$x+1\over\sqrt{1-x^2}$$
Here is a ref inside math: \(\ref{ref2}+1\) and text after it.

\begin{align}
x& = y_1-y_2+y_3-y_5+y_8-\dots
&& \text{by \eqref{ref1}}\\
& = y'\circ y^* && \text{(by \eqref{ref3})}\\
& = y(0) y' && \text {by Axiom 1.}
\end{align}

Here's a bad ref [\ref{ref4}] to a nonexistent label.

An alignment:
\begin{align}
a&=b\label{ref3}\cr
&=c+d
\end{align}
and a starred one:
\begin{align*}
a&=b\cr
&=c+d
\end{align*}