\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that the set \(\mathcal{S}\) of solutions \(y \in C^2(\mathbb{R}, \mathbb{R})\) of the linear homogeneous differential equation \(y'' + y = 0\) is a subspace of \(C^2(\mathbb{R}, \mathbb{R})\).
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