Change the equation number in alignat

Question

I have the following equations with-in alignat environment

$\begin{alignat}{4}
&p^0\colon\od{u_0(x)}{x} = 0 \quad &\text{with} \quad u_0(0) = 1, \\
&p^1\colon \od{u_1(x)}{x} -u_{{0}} \left( x \right) =0 \quad &\text{with} \quad u_1(0) = 0, \\
&p^2\colon \od{u_2(x)}{x} -u_{{1}} \left( x \right) =0 \quad &\text{with} \quad u_2(0) = 0, \\
&p^3\colon \od{u_3(x)}{x} -u_{{2}} \left( x \right) =0 \quad &\text{with} \quad u_3(0) = 0. \\
\end{alignat}$

In my document these equations are numbered as (1), (2), (3) and so-on.

How can I number these equations as (1.1), (1.2), (1.3) without affecting other equations that will come after these equaitons?

Thank you for helping me.

Answer 1

You want to use the subequationsenvironment, as follows:

\documentclass{minimal}
\usepackage{amsmath}
\begin{document}
    \begin{alignat}{2}
        x& = y_1-y_2+y_3-y_5+y_8-\dots &\quad& \text{by C}\\
        & = y’\circ y^* && \text{by D}\\
        & = y(0) y’ && \text {by Axiom 1.}
    \end{alignat}

    \begin{subequations}
        \renewcommand{\theequation}{\theparentequation.\arabic{equation}} 
        \begin{alignat}{4}
            & p^0\colon \od{u_0(x)}{x} = 0 \quad &\text{with} \quad u_0(0) = 1, \\
            & p^1\colon \od{u_1(x)}{x} -u_{{0}} \left( x \right) =0 \quad &\text{with} \quad u_1(0) = 0, \\
            & p^2\colon \od{u_2(x)}{x} -u_{{1}} \left( x \right) =0 \quad &\text{with} \quad u_2(0) = 0, \\
            & p^3\colon \od{u_3(x)}{x} -u_{{2}} \left( x \right) =0 \quad &\text{with} \quad u_3(0) = 0.
    \end{alignat}
    \end{subequations}

    \begin{alignat}{2}
        x& = y_1-y_2+y_3-y_5+y_8-\dots &\quad& \text{by C}\\
        & = y’\circ y^* && \text{by D}\\
        & = y(0) y’ && \text {by Axiom 1.}
    \end{alignat}
\end{document}

which produces the following output: