1. y" - 2y' - 3y = 5e¹, y(0) = 1, y'(0) = 0 2. y" + 2y + 5y = 3 sin(2x) 3. y" - 4y + 4y = -7x+4x², y(0) = 0, y'(0) = 1 - y = -25e²x +7e-2x, y(0) = 1, y'(0) = −1 y(0) = 5, y'(0) = -1 y'(0) = -10 4. 6y" + y 5. y" - 4y + 4y = 25 cos(x), 6. 2y"+y' = 4x, y(0) = 7, 7. y"-3y' - 4y = 5e-, y(0) = 1, 8. y" + 4y = 4 sin(2x) 9. 2y" - 3y' = 9x² +10, y(0) = 1, y'(0) = -3 10. 3y" - 5y' - 2y = 3e² y'(0) = 13

Calculus: Early Transcendentals
8th Edition
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Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Use the method of undetermined coefficients to solve non-homogeneous equations.
Find the solution to the given differential equation. If initial conditions are not given,
find the general solution.
1. y" - 2y3y = 5e¹r, y(0) = 1, y'(0) = 0
2. y" + 2y + 5y = 3 sin(2x)
3. y" - 4y + 4y = -7x+4x², y(0) = 0, y'(0) = 1
4. 6y"+y'-y = -25e²+7e-2x, y(0) = 1, y'(0) = −1
5. y4y + 4y = 25 cos(x), y(0) = 5, y'(0) = -1
6. 2y"+y' = 4x, y(0)=7, y'(0) = -10
7. y" - 3y - 4y = 5e, y(0) = 1,
8. y" + 4y = 4 sin(2x)
9. 2y" - 3y = 9x² +10, y(0) = 1, y'(0) = -3
10. 3y" - 5y'- 2y = 3e²r
y'(0) = 13
Transcribed Image Text:Use the method of undetermined coefficients to solve non-homogeneous equations. Find the solution to the given differential equation. If initial conditions are not given, find the general solution. 1. y" - 2y3y = 5e¹r, y(0) = 1, y'(0) = 0 2. y" + 2y + 5y = 3 sin(2x) 3. y" - 4y + 4y = -7x+4x², y(0) = 0, y'(0) = 1 4. 6y"+y'-y = -25e²+7e-2x, y(0) = 1, y'(0) = −1 5. y4y + 4y = 25 cos(x), y(0) = 5, y'(0) = -1 6. 2y"+y' = 4x, y(0)=7, y'(0) = -10 7. y" - 3y - 4y = 5e, y(0) = 1, 8. y" + 4y = 4 sin(2x) 9. 2y" - 3y = 9x² +10, y(0) = 1, y'(0) = -3 10. 3y" - 5y'- 2y = 3e²r y'(0) = 13
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