left align using alignat?

Question

I want to align some equations on the left side in a document. And additionally I want to have some aligned text behind every equation. Also the equations need to be numbered. With the code below my goal is almost achieved. I just need to bring the text aligned to the right... How do I do that? Thanks

\documentclass[a4paper, 11pt]{book}
\usepackage{amsmath}
\begin{document}
\begin{flalign}
    &u_\mathrm{L} = L \cdot \frac{\text{d}i_\mathrm{L}}{\text{d}t} \quad(\text{Differentialform}) &\label{eq:2_19} \\
    &i_\mathrm{L} = \frac{1}{L} \cdot \int\limits_t u_\mathrm{L} \text{d}t + i_\mathrm{L}(t=0) \quad (\text{Integralform}) &\label{eq:2_20}
\end{flalign}
\end{document}

Answer 1

... or just rearrange ampersands:

\documentclass[a4paper, 11pt]{book}
    \usepackage{amsmath}
\begin{document}
    \begin{flalign}
u_\mathrm{L}    &   = L \cdot \frac{\text{d}i_\mathrm{L}}{\text{d}t}       
    &       
                &   \text{(Differentialform)}       &       &   \\
i_\mathrm{L}    & = \frac{1}{L} \cdot \int\limits_t u_\mathrm{L} \text{d}t + i_\mathrm{L}(t=0)     
    &       
                &   \text{(Integralform)}           &       &   
    \end{flalign}
\end{document} 

Answer 2

It's just a matter of using \mathllapfrom the mathtools package for (part of) the longest equation:

 \documentclass[a4paper, 11pt]{book}

\usepackage{mathtools}

\begin{document}

\begin{flalign}
& u_\mathrm{L} = L · \frac{\text{d}i_\mathrm{L}}{\text{d}t} & & \text{(Differentialform)} & & \label{eq:2_19} \\
& \mathrlap{i_\mathrm{L} = \frac{1}{L} · \int\limits_t u_\mathrm{L} \text{d}t + i_\mathrm{L}(t=0) } & & \text{(Integralform)} & & \label{eq:2_20}
\end{flalign}

\end{document} 

Answer 3

You can use the [fleqn] option to the amsmath pacakge and and control the left indent via the \mathindent length:

Notes:

• The showframe package was used just to show the page margins. It is not needed in your actual use case.

Code:

\documentclass{book}
\usepackage[fleqn]{amsmath}
\usepackage{showframe}

\begin{document}

{%\setlength{\mathindent}{0pt}% <-- brace group to keep these changes local.
\begin{alignat}{3}
    u_\mathrm{L} &= L \cdot \frac{\text{d}i_\mathrm{L}}{\text{d}t} &&\quad(\text{Differential form}) &\label{eq:2_19} \\
   i_\mathrm{L} &= \frac{1}{L} \cdot \int\limits_t u_\mathrm{L} \text{d}t + i_\mathrm{L}(t=0)  &&\quad(\text{Integral form}) \label{eq:2_20}
\end{alignat}
}

\end{document}