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In mt book I saw these two reactions:

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I don't know what is the mechanism for these reactions & that's why I am unable to understand how these products are formed & why they are so different. Please explain the mechanism in detail.

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This might sound obvious, but since the reagent and the reaction conditions are identical, the reason for the different outcome of the reactions must be related to the starting materials.

In the case of the aldoxime, the carbon atom of the former $\ce{CHO}$ group still bears a hydrogen atom.

Together with the $\ce{OH}$ group on the adjacent nitrogen atom, this allows (formally) for the elimination of water from the aldoxime under suitable conditions. High temperatures and the presence of a dehydrating agent facilitate exactly that.dehydration of aldoxime

The formation of a nitile from an aldoxime in boiling acetic anhydride is (formally) a dehydration reaction.

For obvious reacons, this pathway is not possible in the case of the ketoxime.

What is the role of acetic anhydride here?

I mentioned that the formation of nitriles from aldoximes is formally a dehydration. In reality, however, it is more likely that acetic anhydride actually reacts with both oximes.

acylation of oximes

Both the aldoxime and the ketoxime are

acylated. For the ketoxime (R' = alkyl), the story ends here. In the case of the aldoxime (R' = H), a subsequent elimination (of acetic acid) eventually furnishes the nitrile.

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