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1. The differential equation y" + 2xy' + 3y = 0 is a. first order linear O second order linear c. third order linear d. first order nonlinear e. second order nonlinear 2. The differential equation y"' + 2y" + 3yy' – 4xy = sin x is a. first order linear b. second order linear c. third order linear d. first order nonlinear e third order nonlinear 3. An integrating factor for the linear differential equation y' + = x is ax с. 1/х d. 1/x е. 4. The differential equation xydx +[ x²+y² ]ay = 0 is a. exact with solutions **Y 4 y² - c 3 = c. x²y y? 3 x²y, y3 ++c. b. exact with solutions = c. c. exact with solutions 2 @hot exact but having an integrating factor y. e. not exact but having an integrating factor x. 5. For the IVP xy" +y' – x²y = 5, y(1) = 3, y'(1) = 4, a unique solution is guaranteed to exist on the interval a. (2, 5) b. (3, 4) с. (2, оо) @ (0, 2) (0, ∞)

1. The differential equation y" + 2xy' + 3y = 0 is a. first order linear O second order linear c. third order linear d. first order nonlinear e. second order nonlinear 2. The differential equation y"' + 2y" + 3yy' – 4xy = sin x is a. first order linear b. second order linear c. third order linear d. first order nonlinear e third order nonlinear 3. An integrating factor for the linear differential equation y' + = x is ax с. 1/х d. 1/x е. 4. The differential equation xydx +[ x²+y² ]ay = 0 is a. exact with solutions **Y 4 y² - c 3 = c. x²y y? 3 x²y, y3 ++c. b. exact with solutions = c. c. exact with solutions 2 @hot exact but having an integrating factor y. e. not exact but having an integrating factor x. 5. For the IVP xy" +y' – x²y = 5, y(1) = 3, y'(1) = 4, a unique solution is guaranteed to exist on the interval a. (2, 5) b. (3, 4) с. (2, оо) @ (0, 2) (0, ∞)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. The differential equation y" + 2xy' + 3y = 0 is a. first order linear O second order linear c. third order linear d. first order nonlinear e. second order nonlinear 2. The differential equation y' + 2y" + 3yy' – 4xy = sin x is a. first order linear b. second order linear c. third order linear d. first order nonlinear (e third order nonlinear 3. An integrating factor for the linear differential equation y' + 2 = x is (ax b. с. 1/х d. 1/x e. e 4. The differential equation xydx + [x² +y* ]dy = 0 is a. exact with solutions 2+ = c. y3 3 b. exact with solutions x²y y² =C. 3 y3 2 Chot exact but having an integrating factor y. e. not exact but having an integrating factor x. c. exact with solutions ++c. 3 5. For the IVP xy" +y' – x²y = 5, y(1) = 3, y'(1) = 4, a unique solution is guaranteed to exist on the interval x+1 а. (2, 5) b. (3, 4) с. (2, оо) → @ (0, 2)
Transcribed Image Text:1. The differential equation y" + 2xy' + 3y = 0 is a. first order linear O second order linear c. third order linear d. first order nonlinear e. second order nonlinear 2. The differential equation y' + 2y" + 3yy' – 4xy = sin x is a. first order linear b. second order linear c. third order linear d. first order nonlinear (e third order nonlinear 3. An integrating factor for the linear differential equation y' + 2 = x is (ax b. с. 1/х d. 1/x e. e 4. The differential equation xydx + [x² +y* ]dy = 0 is a. exact with solutions 2+ = c. y3 3 b. exact with solutions x²y y² =C. 3 y3 2 Chot exact but having an integrating factor y. e. not exact but having an integrating factor x. c. exact with solutions ++c. 3 5. For the IVP xy" +y' – x²y = 5, y(1) = 3, y'(1) = 4, a unique solution is guaranteed to exist on the interval x+1 а. (2, 5) b. (3, 4) с. (2, оо) → @ (0, 2)
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