How do I achieve this alignment of multiple equations?

Question

Consider the following example:

\documentclass{article}

\usepackage{amsmath, amsthm, amssymb, mathtools, thmtools, unicode-math}

\begin{document}

\begin{align*}
    \hphantom{\Leftrightarrow}Lf&=0\\
    \Leftrightarrow f''&=-\frac{2b}af'\\
    \Leftrightarrow f'&=c_1\exp\left(-2\int_0^{\;\cdot}\frac ba(x)\:{\rm d}x\right)\\
    \Leftrightarrow f&=c_1\int_0^{\;\cdot}\exp\left(-2\int_0^y\frac ba(x)\:{\rm d}x\right)\:{\rm d}y+c_2
\end{align*}

\end{document}

The desired output is as follows:

How can I achieve the correct alignment? Basically, it is a matrix with four columns. The content of the first, second and fourth column should be left, right and left aligned, respectively. How can we do this?

Answer 1

Use alignat:

\documentclass{article}

\usepackage{amsmath}

\newcommand{\diff}{\mathop{}\!\mathrm{d}}

\begin{document}

\begin{alignat*}{2}
&\quad& Lf&=0\\
\Leftrightarrow && f''&=-\frac{2b}af'\\
\Leftrightarrow && f'&=c_1\exp\biggl(-2\int_0^{\;\cdot}\frac ba(x)\diff x\biggr)\\
\Leftrightarrow && f&=c_1\int_0^{\;\cdot}\exp\biggl(-2\int_0^y\frac ba(x)\diff x\biggr)\diff y+c_2
\end{alignat*}

\end{document}

I changed how the differential d is typeset, the spacing with \: is wrong and \rm has been deprecated for more than 20 years.

Answer 2

There's also this possibility, with the \ArrowBetweenLines command, from mathtools.

Unrelated: needless to load amsmath since mathtools already does it for you.

\documentclass{article}

\usepackage{ amssymb, mathtools, amsthm, thmtools, unicode-math}

\begin{document}

\begin{alignat*}{2}
  & & Lf&=0\\
    \ArrowBetweenLines & & f''&=-\frac{2b}af'\\
    \ArrowBetweenLines & &f'&=c_1\exp\left(-2\int_0^{\;\cdot}\frac ba(x)\:{\rm d}x\right)\\
    \ArrowBetweenLines & &f&=c_1\int_0^{\;\cdot}\exp\left(-2\int_0^y\frac ba(x)\:{\rm d}x\right)\:{\rm d}y+c_2
\end{alignat*}

\end{document}