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I would want to use WolframEngine's API to compute motion path equations. For example, a uniform motion's system of equations gives a path equation:

In = DSolve[{s'[t] == v[t], v'[t] == a, s[0] == b, v[0] == c}, {s[t], v[t]}, t]

                2 b + 2 c t + a t
Out = {{s[t] -> ------------------, v[t] -> c + a t}}
                       2

Can I somehow obtain a solution if v'[t] == a is replaced by v'[t] <= a? I know that in this particular case, I can just convert the answer to

         2 b + 2 c t + a t
s[t] <= ------------------, v[t] <= c + a t
                2

but is it possible to make WolframEngine solve systems like that?

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    $\begingroup$ Just assume $aa \le a$ and DSolve[{s'[t] == v[t], v'[t] == aa, s[0] == b, v[0] == c}, {s[t], v[t]}, t] $\endgroup$
    – yarchik
    Jun 17, 2022 at 16:32
  • $\begingroup$ Assuming[aa < a, DSolve[ ... ]] gives the same answer as above, DSolve[..., Assumptions -> aa < a] gives an error, Assuming[aa < a, DSolveValue[ ... ]]` gives only right-hand sides of the solutions $\endgroup$
    – scriptfoo
    Jun 21, 2022 at 9:44

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