My Math Forum differential equation

 Calculus Calculus Math Forum

 June 26th, 2016, 08:08 AM #1 Senior Member   Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 differential equation How to solve the differential equation $$x \frac{d^2y}{dx^2}+2(3x+1)\frac{dy}{dx}+3y(3x+2)=18 x$$ I think I could let $u=xy$, but I don't know how to proceed it. Last edited by skipjack; June 26th, 2016 at 02:01 PM.
 June 26th, 2016, 02:04 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,975 Thanks: 2225 $xy = u$ implies $xy' + y = \dfrac{du}{dx}$ and $x\dfrac{d^2y}{dx^2} + 2\dfrac{dy}{dx} = \dfrac{d^2u}{dx^2}$. Hence $\dfrac{d^2u}{dx^2} + 6\dfrac{du}{dx} + 9u = 18x$. Thanks from topsquark, Country Boy and manus

 Tags differential, equation

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post kkg Calculus 3 April 11th, 2016 10:36 AM mona123 Differential Equations 3 January 21st, 2015 06:27 AM Sonprelis Calculus 6 August 6th, 2014 10:07 AM PhizKid Differential Equations 0 February 24th, 2013 10:30 AM main Differential Equations 1 July 3rd, 2009 09:52 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top