hw5key - AMATH 351 Homework 5 Section7.1 6 Section7,2 15,...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: AMATH 351 Homework 5 Section7.1 6 Section7,2 15, 21, 22 Section7.3 22 Section7.5 2, 11, 31 Section 7.1 6 u 00 + p ( t ) u + q ( t ) u = g ( t ) , u (0) = u , u (0) = u Let u 1 = u, u 2 = u , then the di erential eqn can be written as u 2 + p ( t ) u 2 + q ( t ) u 1 = g ( t ) So the initial value problem is equivalent to ( u 1 = u 2 u 2 =- q ( t ) u 1- p ( t ) u 2 + g ( t ) u 1 (0) = u , u 2 (0) = u Section 7.2 15 1 2 1 1 2 1 1 2 1 1 1 2 1 2 1 1 2 1 2 1 1 2 1- 1 4 1 2- 1 4 1 1 2 1 2 1 1 2 1 1 2- 1 4 1 8 1 1 2 1 2 1 1 2 1 1 2- 1 4 1 8 1 1 2- 1 6 1 1 2 So the inverse matrix is 1 2- 1 4 1 8 1 2- 1 6 1 2 21 A ( t ) = e t 2 e- t e 2 t 2 e t e- t- e 2 t- e t 3 e- t 2 e 2 t , B ( t ) = 2 e t e- t 3 e 2 t- e t 2 e- t e 2 t 3 e t- e- t- e 2 t (a) A + 3 B = e t 2 e- t e 2 t 2 e t e- t- e 2 t- e t 3 e- t 2 e 2 t + 3 2 e t e- t 3 e 2 t...
View Full Document

Page1 / 6

hw5key - AMATH 351 Homework 5 Section7.1 6 Section7,2 15,...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online