Differential Equations Ordinary and Partial Differential Equations Math Forum

 October 10th, 2015, 03:02 AM #1 Newbie   Joined: Sep 2015 From: AU Posts: 5 Thanks: 0 2nd Order diff (PLZ HELP ! :D) How do i approach this question?? Imgur: The most awesome images on the Internet Imgur: The most awesome images on the Internet (it's not letting me embed the image so here are the links) I got a) as my" + By' =mg however can't solve for part b) Any help would be greatly appreciated!! Thank you！！！！！ October 28th, 2015, 05:45 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 This is a linear non-homogeneous differential equation with constant coefficients. Its associated homogeneous equation is $\displaystyle my''+ \beta y'= 0$ which has "characteristic equation" $\displaystyle mr^2+ \beta r= r(mr+ \beta)= 0$. The roots of that are $\displaystyle r= 0$ and $\displaystyle r= -\frac{\beta}{m}$. That means that the general solution to the associated homogeneous equation is $\displaystyle y(t)= C_1e^{0t}+ C_2e^{-\frac{\beta}{m}t}= C_1+ C_2e^{-\frac{\beta}{m}t}$. Since the "non-homogeneous" part, -g, is constant, normally, we would try a constant, A, as a solution to the entire equation. But a constant is already a solution to the associated homogeneous equation so we try y= At instead. With y= At, y'= A and y''= 0 so the equation becomes $\displaystyle m(0)+ \beta(A)= -g$ and $\displaystyle A= -\frac{g}{\beta}$. The general solution to the differential equation is $\displaystyle y(t)= C_1+ C_2e^{-\frac{\beta}{m}t}- \frac{g}{\beta}t$. Tags 2nd, diff, order, plz 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 mikehepro Calculus 2 October 10th, 2015 05:24 AM arogyth Applied Math 0 July 22nd, 2013 01:22 PM arogyth Calculus 1 July 22nd, 2013 01:19 PM mathkid Calculus 5 September 10th, 2012 03:10 PM foy1der Calculus 2 February 2nd, 2010 07:27 PM

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