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October 10th, 2015, 02:58 AM   #1
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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.
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October 10th, 2015, 03:10 AM   #2
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Quote:
Originally Posted by mikehepro View Post
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 $\displaystyle y(t)= C_1+ C_2e^{-\frac{B}{m}t}+ \frac{mg}{B}$.
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October 10th, 2015, 05:24 AM   #3
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There's a $\displaystyle t$ missing from the final term.
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