TTU - MATH 3350 - MATH 3350_ EXAM 2 Review - Study Guide

View Full Material##### School: Texas Tech University

##### Department: Math

##### Course: Higher Mathematics for Scientists & Engineers 1

##### Term: Spring 2017

##### Tags: Math3350, Euler's Method, ConstantCoefficients, Nonhomogenous, and Linear Equations

##### Name: MATH 3350_ EXAM 2 Review

##### Description: This is the review for exam 2 on this Friday. This exam will be difficult if you don't prepare well. In each method that we learned in the class, I highlight the important information and also did some examples. If something is not clear, please send me an email, I would like to help.

##### Uploaded: 03/20/2018

**3**Pages

**22**Views

**17**Unlocks

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##### School: Texas Tech University

##### Department: Math

##### Course: Higher Mathematics for Scientists & Engineers 1

##### Term: Spring 2017

##### Tags: Math3350, Euler's Method, ConstantCoefficients, Nonhomogenous, and Linear Equations

##### Name: MATH 3350_ EXAM 2 Review

##### Description: This is the review for exam 2 on this Friday. This exam will be difficult if you don't prepare well. In each method that we learned in the class, I highlight the important information and also did some examples. If something is not clear, please send me an email, I would like to help.

##### Uploaded: 03/20/2018

**3**Pages

**22**Views

**17**Unlocks

- Better Grades Guarantee
- 24/7 Homework help
- Notes, Study Guides, Flashcards + More!

Unformatted text preview: Exam 2 Review 1) Give the interval of existence of the unique solution to the initial value problem A (x-36 12 y - xy +244 9 = ICs y (2): 3, y'(2) --2 , y"(2) = 4 , y "(2) = 0 y"(2): 0 - x - 36 - 0 -6 -4.2 2 Dis conhnui ftes od: + 3 + 2 = 0 3 =- 2 + 2+4 = 0 _) a = -4 + x +1>0 (always!) . Initial point ad a. - 2 => -24x < 6 19 Al ShadySoup A Study soul Study o Study soup Study Soup2) Solve the Inih al value pro blem e - When the constant coefficients > use Linear, Homogeneous , constant coefficient method A saysoup Lay' + by' + c = D constant number Ex. ly" +ly' - 2y = 0 , 4 (0) - 4, y'(o) = 1 |(1,1, - 2 ) constant coefficients y" + y' - 2y = 0 r +r - 2 = 0 (r+2)(r - 1) = 0 =) r=-2, 1 4 + 2 = 0, 09 >' + y ex = P2 -> y = ye"x + c,aera r= * + Br ->y = ct exacos (Pac) +c, ex sin(B 5) . We have C2 y = 9e + cp E 20 y' = get - 2c, e-2x Study A Study Soup study soup4 (0) - 4 - C + C2 = A y'(0) = 1 -> le, 209 - 1 -> C + 202 = 4-1 32 = 3 C2 : 1 - = 3 30, e 22 3) Find the gener al solution (HW07, 08 ) r2 - 2(1) + L= 0 =>r = 1 + 3i (A study sour -> y = C ea cos(PX) + C, et sin (br) y = C, e cos (2x) + ca eto s:0 (3x) E 2 y" + 8y'+ 16 = 0 r + 8r + 16 = 0 r + 24) +42 = 0 (r +4)2 = 0 C = -4,-4 n = 2-4 y = C4 4x + ca 20 e 40 A study soup A studyson udy soup Study Soup

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