Here is a statment in my book:
"Let $W_{\mathrm{x}}$ denote Wiener measure starting at $\mathrm{x}$ on $\Omega=\mathrm{C}\left([0, \mathrm{T}], \mathbb{R}^{\mathrm{n}}\right), \mathrm{T}<\infty,$ and let $W=\int W_{\mathrm{x}} \mathrm{d} \mathrm{x}$ be the stationary Wiener measure.
We denote by $\mathbb{D}$ the set of all probability measures on $\Omega$ which are equivalent to the stationary Wiener measure. Let $F_{\mathrm{t}}$ be the $\sigma$ -algebras of events observable up to time $t$. By Girsanov's theorem, any $P \in \mathbb{D}$ has a forward drift $\beta_{t}^{P},$ in the sense that, under $P,$ the coordinate process admits the representations $$ \begin{array}{ll} \mathrm{dX}_{\mathrm{t}}=\beta_{\mathrm{t}}^{\mathrm{P}} \mathrm{d} \mathrm{t}+\mathrm{d} \mathrm{W}_{\mathrm{t}}, & \beta_{\mathrm{t}}^{\mathrm{P}} \text { is } F_{\mathrm{t}} \text { -measurable, } \end{array} $$
where $W_t$ is the standard Wiener processes adapted to $F_t$ ."
How can we use Girsanov to show this ? This is basically saying that if a process $X_t$ induces a measure on $C[0,T]$ that is equivalent to the Wiener measure, then it must satisfy the above SDE.
You can find Girsanov's theorem in the form we need in this paper or in this one.
It is confusing if you never saw "part b)" of the theorem in the first paper which is not on Wikipedia I believe. But so what you're saying is verbatim what the theorem says.