The synonym of occupied is busy.
Other synonyms of busy are engaged, working, employed, at work, on the job, hard-pressed, active. absorbed, engrossed, interested, involved, focused on, immersed, preoccupied. informal tied up, hard at it, wrapped up, on the go, on the trot.
Indisposed means not available.
To use Indisposed in a sentence can be.
The student didn't show up to school today because he was indisposed and not feeling well.
The teacher didn't show up today because she was indisposed.
When someone is indisposed it means they are unavailable because of being sick, too busy or unwilling to do something.
Indisposed means that you're not feeling very well or you're not available or you're not willing to do something.
If you say that someone is indisposed, you mean that they are not available because they are ill, or for a reason that you do not want to reveal.
Some ways to use Indisposed in a sentence are.
We are informed that he has been indisposed for the last few days.
I feel very indisposed to limit in any way the discretion which those bodies now enjoy.
She would have wished to be here today to make her own contribution, but she is indisposed.
I'm not going to work today as I'm indisposed.
Or he didn't show up today to work because he was indisposed.
The word Indisposed is a rather formal word, and, as a result, is sometimes used in a mocking or joking way.
For example, the phrase "temporarily indisposed" is occasionally used as a humorous euphemism for "in the bathroom." ("Indisposed" in this context is used with its other meaning of "slightly ill.")
The adjective indisposed is a slightly formal way to describe someone who's feeling sick.
You might call your boss to tell her that you can't make it to work because you're indisposed.
When you're a bit under the weather, you're indisposed, particularly if you're ill enough to stay in bed and miss work or school.