Let $(M,g)$ be a Riemannian manifold, and $x\in M$ be a fixed point.

Q Can we find a conformal transformation such that near $x$ we can write $e^{2u}g$ as $(dx^1)^2+\cdots+(dx^n)^2$?

Since the question is local, we can replace $M$ with $\mathbb R^n$.

(PS: Any reference is welcome.)