June 1st, 2014, 05:47 PM  #1 
Member Joined: Sep 2013 Posts: 43 Thanks: 0  Taylor series
I have a differential equation dh/dt=h^2 and h(0)=h0 exact solution is h(t)=h0/(th0+1) but if written in taylor expansion is h(0+t)=h0+h'(0)(t)+t^2h"(0)/2 and so on how to find the second derivative and so on? quite confuse on this. 
June 1st, 2014, 06:47 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,399 Thanks: 2477 Math Focus: Mainly analysis and algebra 
$$\frac{d^2h}{dt^2} = \frac{d}{dt} \frac{dh}{dt} = \frac{d}{dt} h^2 = 2h\frac{dh}{dt}$$ by the chain rule. You know $\frac{dh}{dt}$ already, so you can substitute that in and proceed as far as you need to. 

Tags 
series, taylor 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Taylor series  milly2012  Calculus  2  March 8th, 2014 04:45 AM 
In need of help disk, series test, taylor, and power series  g0bearmon  Real Analysis  2  May 22nd, 2012 12:10 PM 
Taylor Series  sonicdashbob  Real Analysis  7  December 6th, 2009 03:46 AM 
Taylor series...  Raidan  Calculus  1  May 4th, 2009 02:00 PM 
In need of help disk, series test, taylor, and power series  g0bearmon  Calculus  1  December 31st, 1969 04:00 PM 