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+ y = e In t 16. 2y" + 2y' + y = 4Vx 17 3x" 6y' + 6y = e* sec r

+ y = e In t 16. 2y" + 2y' + y = 4Vx 17 3x" 6y' + 6y = e* sec r

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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Solve #16 by using variation of parameters
**Chapter 4: Higher-Order Differential Equations** Here are several differential equations for practice and study: 11. \( y'' + 3y' + 2y = \frac{1}{1 + e^x} \) 12. \( y'' - 2y' + y = \frac{e^x}{1 + x^2} \) 13. \( y'' + 3y' + 2y = \sin e^x \) 14. \( y'' - 2y' + y = e^t \arctan t \) 15. \( y'' + y = e^{-t} \ln t \) 16. \( 2y'' + 2y' + y = 4\sqrt{x} \) 17. \( 3y'' - 6y' + 6y = e^x \sec x \) 18. \( 4y'' - 4y' + y = e^{x/2} \sqrt{1 - x^2} \) **Problems 19-22:** For these problems, solve each differential equation using the method of variation of parameters, with the initial conditions \( y(0) = 1 \) and \( y'(0) = 0 \). 19. \( 4y'' - y = xe^{x/2} \) 20. \( 2y'' + y' - y = x + 1 \)
Transcribed Image Text:**Chapter 4: Higher-Order Differential Equations** Here are several differential equations for practice and study: 11. \( y'' + 3y' + 2y = \frac{1}{1 + e^x} \) 12. \( y'' - 2y' + y = \frac{e^x}{1 + x^2} \) 13. \( y'' + 3y' + 2y = \sin e^x \) 14. \( y'' - 2y' + y = e^t \arctan t \) 15. \( y'' + y = e^{-t} \ln t \) 16. \( 2y'' + 2y' + y = 4\sqrt{x} \) 17. \( 3y'' - 6y' + 6y = e^x \sec x \) 18. \( 4y'' - 4y' + y = e^{x/2} \sqrt{1 - x^2} \) **Problems 19-22:** For these problems, solve each differential equation using the method of variation of parameters, with the initial conditions \( y(0) = 1 \) and \( y'(0) = 0 \). 19. \( 4y'' - y = xe^{x/2} \) 20. \( 2y'' + y' - y = x + 1 \)
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