Differential Equations Lecture Work Solutions 312

Differential Equations Lecture Work Solutions 312 - u n 2 =...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
u 3 2 =1+1 1 4 = 7 4 , compare this to n =3inthesum u 4 2 =1+ 3 2 3 4 + 1 8 = 15 8 , compare this to n =4inthesum In general for r = 1 4 we have u n 2 = 1 2 u n 1 2 +1 This is a nonhomogeneous diFerence equation. The general solution of the homogeneous is u n 2 = 1 2 ± n A particular solution for the nonhomogeneous is a constant, which when substituted in the equation turn out to be 2, so
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: u n 2 = 1 2 n + 2 Upon letting n we get the steady state u 2 = 2 If we look at the limit for the innite series, note that this innite series is geometric with rst term 1 and quotient 1 2 . Thus the sum is 1 1 1 2 = 2 the same as before. 312...
View Full Document

Ask a homework question - tutors are online