
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 10th, 2014, 10:44 AM  #1 
Senior Member Joined: Nov 2013 Posts: 137 Thanks: 1  Solutions for diff equation in form of series
Given the following diff equation: , being D = d/dx, the "implicit" solution is: , so, for "explicit" the solution is necessary to expand the fraction 1/(1D) by identity: , but this infinity series is true only for x<1, for x>1 is necessary utilize the following series: . Happens that D isn't a number for I say that D is less or greater than 1. So, how can I interprate this form of solution correctly? PS, this ideia from Operational Calculus: https://es.wikipedia.org/wiki/Transf...hist.C3.B3rica Heaviside’s Operational Calculus  Rip's Applied Mathematics Blog 
May 10th, 2014, 11:32 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra 
D is an operator. You can't leave it with nothing to operate on. If I were solving that with a series, I'd say $Dy(x) = y(x)  f(x)$ and then crreate a Taylor series. Of course, this relies on having an initial condition. Then $y(x) = y(0) + Dy(0)x + \cdots = y(0) + (y(0)  f(0)x + \cdots$ We can get $D^2y(x)$ and higher orders by differentiating the equation for $Dy(x)$. Edit: having browsed the blog, I think I've seen something similar before. I would rather understand why it works than the approach seen there, where it seems to for my functions, so lets say it's right. Last edited by v8archie; May 10th, 2014 at 11:49 AM. 
May 10th, 2014, 12:59 PM  #3  
Senior Member Joined: Nov 2013 Posts: 137 Thanks: 1  Quote:
 
May 10th, 2014, 04:59 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra 
Shouldn't you write $$(1 D)y = f(x) \Longrightarrow y = \frac{1}{D1}f(x)$$ and then proceed as in the blog? 
May 11th, 2014, 04:54 AM  #5  
Senior Member Joined: Nov 2013 Posts: 137 Thanks: 1  Quote:
PS: look this article from page 13 until 17. http://www.latp.univmrs.fr/~chaabi/...20,2006%29.pdf  

Tags 
diff, equation, form, series, solutions 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Power Series Solutions for a DE  solrob  Applied Math  1  October 14th, 2013 11:47 AM 
Find the diff equation of family of circles with center on t  gen_shao  Calculus  3  July 9th, 2013 12:52 PM 
Series solutions to ODE  Grayham1990  Complex Analysis  2  March 24th, 2012 05:57 PM 
SOLVE THE DIFF.EQUATION  zgonda  Calculus  1  November 27th, 2010 04:23 PM 
Series Solutions to Differential Equations  cmmcnamara  Differential Equations  0  February 25th, 2010 08:41 AM 