1. In contexts of Time

i) IN is used before a noun denoting a period of time referring to AT THE END OF
ii) WITHIN is used before a noun denoting of time referring to BEFORE THE END OF

a) I’ll leave home in two hours. (means after the period of two hours has ended)
b) I’ll leave home within two hours. (means before the period of two hours has ended)
c) I’ve booked train tickets on the Internet. They should arrive within three days. (means no later than three days from now)
d) I’ve noticed her change within a very short time.

2. In contexts of Space

WITHIN = not further than a particular area or space. WITHIN does not mean the same as IN. Within stresses that something is not further than a particular area or space; e.g.

a) People who live within the city pay higher local taxes than people who live just outside the city. (= the people who live no further than the city boundary or limits)

b) We’ve always lived within ten miles of the coast. We love the sea. (We’ve always lived no further than ten miles from the coast.)

INCORRECT: Your shirt is within the drawer.
CORRECT: Your shirt is in the drawer.

For more chapters/topics on English Grammar read the following book authored by me.

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For English Practice Sets on various topics read the following book authored by me.

Link for buying the above book