This preview shows page 1. Sign up to view the full content.
Unformatted text preview: x p t ( ) = C , must resemble form of righthand side, which is 0 plug into equation to find C : C + 5 C + 6 C = 6 , C = 1 , x p t ( ) = 1 Genera solution is sum of two. x t ( ) = x h t ( ) + x p t ( ) = A 1 e 2 t + A 2 e 3 t + 1 Now plug in initial conditions x ( ) = A 1 e 2 + A 2 e 3 + 1 = A 1 + A 2 + 1 = x ( ) = 2 A 1 e 2 t t = 3 A 2 e 3 t t = = 2 A 1 + 3 A 2 = A 1 = 3 2 A 2 , 3 2 A 2 + A 2 + 1 = 1 2 A 2 = 1 , A 2 = 2 , A 1 = 3 a. x t ( ) = 3 e 2 t + 2 e 3 t + 1 for t b. For an n th order differential equation, the characteristic equation will have n roots, and so there will be n (complex) exponentials in the homogeneous solution. c. (iv) After. Always remember to plug in initial conditions at the very end....
View
Full
Document
This note was uploaded on 11/22/2011 for the course ME ME360 taught by Professor Kuo during the Fall '11 term at University of Michigan.
 Fall '11
 KUO

Click to edit the document details