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 April 20th, 2016, 04:27 AM #1 Newbie   Joined: Apr 2016 From: England Posts: 2 Thanks: 0 Rewriting second order to 1st order diff eqn Hi I need to apply the ralston 2nd order method to find an approximate value for y(2) of the following differential equation: xy'' - y' = x^2 + x With initial conditions y(1) = 1 and y'(1) = 5 So far I have done z1=y, z2=y' and z3=y'', resulting in the equation xz2' = x^2 + x + z2 This equation finds an approximate value for y'(x), but I need a value for y(x) how can I advance from this? April 20th, 2016, 06:00 AM #2 Senior Member   Joined: Aug 2011 Posts: 334 Thanks: 8 xy''-y'=x^2+x Change of unknown function : z(x)=y' xz'-z=x^2+x First order linear ODE easy to solve. April 20th, 2016, 06:45 AM   #3
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 Originally Posted by JJacquelin xy''-y'=x^2+x Change of unknown function : z(x)=y' xz'-z=x^2+x First order linear ODE easy to solve.
JJacquelin
How would I be able to find an approximation of y(x) using that equation? Wouldn't I only be able to approximate y'(x) by using my second initial condition? April 22nd, 2016, 08:28 AM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 The point is that you have two first order equations for y and z: $\displaystyle xz'- z= x^2+ x$ and $\displaystyle y'= z$. Once you have solved the first equation for z, using whatever numerical method you prefer, then do a (numerical) integration to find y. April 22nd, 2016, 07:14 PM #5 Global Moderator   Joined: Dec 2006 Posts: 21,030 Thanks: 2260 [QUOTE=Don96;532996]I need to apply . . . /QUOTE] What was the original wording of the question? Tags 1st, diff, eqn, order, rewriting 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 mikehepro Differential Equations 1 October 28th, 2015 05:45 AM mikehepro Calculus 2 October 10th, 2015 05:24 AM hanilk2006 Calculus 1 October 2nd, 2013 05:01 PM mathkid Calculus 5 September 10th, 2012 03:10 PM foy1der Calculus 2 February 2nd, 2010 07:27 PM

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