@Kitonum 

If I use your new example it works, but only one time.
After the first calculation everything is ok.
After the second calculation I get the following error:
Error, (in x) invalid input: rhs received sol(t)[2], which is not valid for its 1st argument, exp

After a maple server restart I'm able to calculate it again.
Is this a known problem?

And I have very small differences between option 1 and option 2.
In option 1, I want to get d2/dt2. This is your example.
In option 2, I don't want to get d2/dt2.
In my opinion, the results of x(t) and d/dt x(t) should be the same, correctly? But they aren't.

What is the reason of this differences?

@Kitonum

I tested your answer but there is a problem: