The Stacks project

Exercise 111.33.8. Given an example of a pair of affine schemes $(X, {\mathcal O}_ X)$, $(Y, {\mathcal O}_ Y)$, an open subscheme $(U, {\mathcal O}_ X|_ U)$ of $X$ and a morphism of schemes $(U, {\mathcal O}_ X|_ U) \to (Y, {\mathcal O}_ Y)$ that does not extend to a morphism of schemes $(X, {\mathcal O}_ X) \to (Y, {\mathcal O}_ Y)$.