Equivalent Definition of injective $R$-module using exact sequences

Question

We call an $R$-module $D$ injective if one of the two equivalent conditions holds:

1. If $0 \rightarrow A \rightarrow B \rightarrow C \rightarrow 0$ is an exact sequence of $R$-modules then the induced sequence $0 \rightarrow \operatorname{Hom}(C,D) \rightarrow \operatorname{Hom} (B,D) \rightarrow \operatorname{Hom} (A,D) \rightarrow 0$ is also exact.
2. Every short exact sequence $0 \rightarrow D \rightarrow Y \rightarrow X \rightarrow 0$ of $R$-modules splits.

I was able to prove 1. $\implies$ 2. but unable to prove the other direction. I don't know what short exact sequence $0 \rightarrow D \rightarrow Y \rightarrow X \rightarrow 0$ I should consider for the converse direction. If possible a answer that is not using Category theory would be helpful.