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 October 10th, 2015, 02:58 AM #1 Newbie   Joined: Sep 2015 From: AU Posts: 5 Thanks: 0 Second order diff question (plz help) How do i approach this question?? http://imgur.com/iZUS77u http://imgur.com/wncJkrT I got a) as my" + By' =mg however can't solve for part b) Any help would be greatly appreciated!! Thank you！！！！！ Last edited by mikehepro; October 10th, 2015 at 03:00 AM. October 10th, 2015, 03:10 AM   #2
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 Originally Posted by mikehepro How do i approach this question??  I got a) as my" + By' =mg however can't solve for part b) Any help would be greatly appreciated!! Thank you！！！！！
I can't see either of your images.. However, to solve my''+ By'= mg, start by finding the characteristic equation to the associated homogenous equation, my''+ By'= 0. The characteristic equation is mr^2+ Br= r(mr+ B)= 0 which has roots 0 and -B/m. So the general solution is $\displaystyle C_1e^{0t}+ C_2e^{-\frac{B}{m}t}= C_1+ C_2e^{-\frac{B}{m}t}$.

Now we look for a single function that satisfies the entire equation. The right hand side, mg, is a constant so, normally, we would try a constant function, A. But a constant function is already a solution so instead we try y= At. Perhaps that was where you had the difficulty. Then y'= A and y''= 0 so the equation m(0)+ BA= mg so that A= mg/B. The general solution to the entire equation is $\displaystyle y(t)= C_1+ C_2e^{-\frac{B}{m}t}+ \frac{mg}{B}$. October 10th, 2015, 05:24 AM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra There's a $\displaystyle t$ missing from the final term. Tags diff, order, plz, question 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 arogyth Applied Math 0 July 22nd, 2013 01:22 PM mathkid Calculus 5 September 10th, 2012 03:10 PM lu5t Applied Math 0 April 30th, 2012 09:59 AM foy1der Calculus 2 February 2nd, 2010 07:27 PM hanilk2006 Abstract Algebra 0 December 31st, 1969 04:00 PM

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