Differential Equations Ordinary and Partial Differential Equations Math Forum

 June 4th, 2013, 04:37 PM #1 Newbie   Joined: May 2013 Posts: 3 Thanks: 0 Need help differential equations? How do you solve a differential equation with variable coefficients, like the equation y''-4xy'+2y=0 for example? None of the ways I know to solve it work. June 4th, 2013, 10:36 PM   #2
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Re: Need help differential equations?

Quote:
 Originally Posted by Antuanne How do you solve a differential equation with variable coefficients, like the equation y''-4xy'+2y=0 for example? None of the ways I know to solve it work.
Try infinite series.
The solutions of many differential �quations cannot be expressed with a finite number of elementary functions. Some solutions can be expressed on the form of infinite series. Some infinite series are known on closed form as special functions.
For example, the closed forms of the solutions of the equation y''-4xy'+2y=0 requires to know the confluent hypergeometric functions of first and second kind (Kummer and Tricomi functions) June 6th, 2013, 09:10 AM #3 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Need help differential equations? Let as JJacqueline suggested. Then (Do you see that the n= 0 terms is 0?) So the equation becomes The "n" in each of these sums is a "dummy index" that has meaning only in the sum. So we can change each index at will In the first sum, let i= n- 2, Then n= 2 gives i= 0, and n= i+ 2 so and . In the last two sums, let i= n so we have For those sums to be 0, the sum for each separate i must be 0. For i= 0 that means we must have For i> 0 we must have . Those are recursive equations for the coefficients. Tags differential, equations Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post rishav.roy10 Differential Equations 0 August 21st, 2013 06:59 AM giga.chalauri Differential Equations 2 April 3rd, 2013 11:34 AM thebigbeast Differential Equations 2 September 11th, 2012 10:27 AM Matt Differential Equations 1 November 13th, 2009 02:34 AM _TJ_ Differential Equations 1 August 29th, 2009 07:08 PM

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