Problem

(a) Evaluate $ \lim_{x \to ^x} x \sin \frac {1}{x…

04:32

Problem 53 Hard Difficulty

Find constants $ A $ and $ B $ such that the function $ y = A \sin x + B \cos x $ satisfies the differential equation $ y" + y' - 2y = \sin x. $

Name: find constants a and b such that the function y a sin x b cos x satisfies the differential equation
Uploaded: 2019-12-15
Duration: 3 min 14 s
Channel: Numerade
Description: Find constants $ A $ and $ B $ such that the function $ y = A \sin x + B \cos x $ satisfies the differential equation $ y" + y' - 2y = \sin x. $

Answer

$A=-\frac{3}{10}, \quad B=-\frac{1}{10}$

Catherine R.

Missouri State University

Kayleah T.

Harvey Mudd College

Michael J.

Idaho State University

Joseph L.

Boston College

Watch More Solved Questions in Chapter 3

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Video Transcript

It's Claire's, the one you married here. So we have. Why is equal to a sign minus B sign. We're gonna differentiate. Get a co sign minus B Sign we differentiate again. We got negative A sign minus b co sign. So when we substitute, we get the second derivative. Thus, the first derivative minus two. Why? It's equal to sign the nine week put negative, eh? Sine x minus b co sign waas a co sign minus b sign minus two times a sign must be co sign and it's equal to sign when we simplify and we get okay minus three b. No sign. Plus negative three A minus B I'm sign, which is equal to zero. I'm school sign. It was one time sign. No, we look at both sides. We have the equations, which is a minus three b equals Sarah Negative. Three a minus B people's one. So we're gonna find be in a So you get three a my next 93 My next three a minus b equals one. We get b is equal to negative one time and A is equal to negative. Three time

Clarissa N.

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions