For each of the exercises given below, verify that the given function (implicit or explicit) is ...

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For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.
\[
y=a e^{x}+b e^{-x}+x^{2}
\]
\[
x \frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d x}-x y+x^{2}-2=0
\]
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