# Find higher order derivatives with DSolve

Posted 9 years ago
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 When I have a differential equation like DSolve[{ x'''''''[t] == d7, x'''''' == d6, x''''' == d5, x'''' == d4, x''' == d3, x'' == d2, x' == d1, x == d0}, x[t], t] I can easiliy solve for x[t]. When I look for x'[t], x''[t] or some higher order derivative I would have to rewrite the expression by moving the d#'s one line down so x[t] becomes x'[t], but this generates a lot of code.Is there a command for getting x'[t] and so on directly? I didn't find a hint in the documentation... With NDSolve it is easy, but with DSolve I'm stuck. Attachments:
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Posted 9 years ago
 Thanks, I didn't know that. I just realized that then it's also possible to have Sqrt''''[x] etc., Problem fixed.
Posted 9 years ago
 Perhaps In:= Clear[x] In:= x[t_] = x[t] /. Apart[DSolve[{x'''''''[t]==d7, x''''''==d6, x'''''==d5, x''''==d4, x'''==d3, x''==d2, x'==d1, x==d0}, [t], t]][] Out= d0 + d1 t + (d2 t^2)/2 + (d3 t^3)/6 + (d4 t^4)/24 + (d5 t^5)/120 + (d6 t^6)/720 + (d7 t^7)/5040 In:= x'[t] Out= d1 + d2 t + (d3 t^2)/2 + (d4 t^3)/6 + (d5 t^4)/24 + (d6 t^5)/120 + (d7 t^6)/720 In:= x'''''[t] Out= d5 + d6 t + (d7 t^2)/2