Here is a labeled equation:
$$x+1\over\sqrt{1-x^2}\label{eq1}$$
and another one equation:
$$\frac{1}{3}\cdot\sum_{i=1}^{n} x^{3} \nonumber $$
This is equation test:
\begin{equation}
f(x)=\dfrac{ax^2+bx+c}{e^{x+2}}
\end{equation}
This is an alignment test:
\begin{align*}
x&= y_1-y_2+y_3-y_5+y_8-\dots \\
&= y(0) y'\; \text{by Axiom 1.} \\
&= \text{by Eq.\eqref{eq1}} \\
&= y'\times y^\frac{n}{2} \\
\end{align*}