Calculus Calculus Math Forum

 June 26th, 2016, 09:08 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 03:01 PM. June 26th, 2016, 03:04 PM #2 Global Moderator   Joined: Dec 2006 Posts: 21,132 Thanks: 2340 $xy = u$ 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 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 kkg Calculus 3 April 11th, 2016 11:36 AM mona123 Differential Equations 3 January 21st, 2015 07:27 AM Sonprelis Calculus 6 August 6th, 2014 11:07 AM PhizKid Differential Equations 0 February 24th, 2013 11:30 AM main Differential Equations 1 July 3rd, 2009 10:52 AM

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