1. You can grow several centimeters in a short time.

2. You can grow by several centimeters in a short time.

(Are both OK? Is 'grow' a transitive verb or an intransitive verb? Is 'by' missing after 'grow' in #1?)

Grow is a transitive active verb.

The first sentence is the better one.

2. You've grown since the last time I saw you!

(Isn't 'grown' used as an intransitive verb here? the past participle of 'grow')

Yes... have grown is intransitive

Check this site:

http://www.chompchomp.com/terms/intransitiveverb.htm

Both sentences are grammatically correct, but they have slightly different meanings.

1. "You can grow several centimeters in a short time."
In this sentence, "grow" is used as an intransitive verb. It means that you can experience a growth in height without specifying the exact means or method of growth. This sentence suggests that growing taller is possible naturally or through factors such as good nutrition, exercise, or genetics.

2. "You can grow by several centimeters in a short time."
In this sentence, "grow" is used as a transitive verb. The addition of "by" indicates the manner or extent of growth. Here, it emphasizes that the growth is specifically by several centimeters. This sentence implies a deliberate action or a specific method to induce the growth, such as with the use of height-enhancing supplements or medical procedures.

So, both sentences are correct, but they convey slightly different meanings and interpretations. And no, "by" is not missing in the first sentence; it is not required because "grow" is used as an intransitive verb.