My Math Forum Second order diff question (plz help)

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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.

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