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# Find higher order derivatives with DSolve

Posted 10 years ago
 When I have a differential equation like DSolve[{ x'''''''[t] == d7, x''''''[0] == d6, x'''''[0] == d5, x''''[0] == d4, x'''[0] == d3, x''[0] == d2, x'[0] == d1, x[0] == 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 10 years ago
 Perhaps In[1]:= Clear[x] In[2]:= x[t_] = x[t] /. Apart[DSolve[{x'''''''[t]==d7, x''''''[0]==d6, x'''''[0]==d5, x''''[0]==d4, x'''[0]==d3, x''[0]==d2, x'[0]==d1, x[0]==d0}, [t], t]][[1]] Out[2]= 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[3]:= x'[t] Out[3]= d1 + d2 t + (d3 t^2)/2 + (d4 t^3)/6 + (d5 t^4)/24 + (d6 t^5)/120 + (d7 t^6)/720 In[4]:= x'''''[t] Out[4]= d5 + d6 t + (d7 t^2)/2 
Posted 10 years ago
 Thanks, I didn't know that. I just realized that then it's also possible to have Sqrt''''[x] etc., Problem fixed.
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