itemize not aligning items

Question

Why are my 2 items not aligning properly?

\newtheorem{ex}{Exercise}

\begin{ex}
\textup{Consider the differential equation
\begin{align}
\label{eq3}
    \frac{x}{y(x)}y'(x)+1=y(x)\,\textup{log}(x)
\end{align} with unknown quantity $y:(0,+\infty)\rightarrow\mathbb{R^*}$.
\begin{itemize}
    \item Show that Equation \eqref{eq3} is a Bernoulli-type differential equation and that $z(x):=\frac{1}{y(x)}$ satisfies
    \begin{align}
    \label{eq4}
        z'(x)-\frac{z(x)}{x}=-\frac{log(x)}{x}\ .
    \end{align}
    \item Find all the solutions to Equation \eqref{eq4} on (0,+\infty).
\end{itemize}}
\end{ex}\hfill\break

Answer 1

The misalignment is a consequence of

Find all the solutions to Equation \eqref{eq4} on (0,+\infty).

as \infty is a math-mode command. Compiling your code results in a classic Missing $ inserted error: never, ever ignore errors! TeX tries to recover but whatever PDF output you get is usually rubbish, as you've seen.

Another couple of comments:

• Don't use \textup{log} but rather \log: the latter has the correct operator spacing, and you need no explicit \, in front of it.
• : is a relational symbol; for a puctuation colon as in this case use \colon.
• Avoid align for single-line equations.
• Avoid wrapping the whole environment content in \textup; use a theorem style which uses upright text from the very beginning.

\documentclass{article}

\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\theoremstyle{definition} % predefined style with upright text
\newtheorem{ex}{Exercise}

\providecommand*{\coloneq}{\mathrel{\mathop:}=}

\begin{document}

\begin{ex}
Consider the differential equation
\begin{equation}
\label{eq3}
    \frac{x}{y(x)} \, y'(x)+1=y(x)\log(x)
\end{equation}
with unknown quantity $y\colon(0,+\infty)\rightarrow\mathbb{R}^*$.
\begin{itemize}
    \item Show that Equation \eqref{eq3} is a Bernoulli-type differential equation
    and that $z(x)\coloneq\frac{1}{y(x)}$ satisfies
    \begin{equation}
    \label{eq4}
        z'(x)-\frac{z(x)}{x}=-\frac{\log(x)}{x}\ .
    \end{equation}
    \item Find all the solutions to Equation \eqref{eq4} on $(0,+\infty)$.
\end{itemize}
\end{ex}

\end{document}