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15. y" - 4y' + 3y = 0; y(0) = 1, y'(0) = 1/3

15. y" - 4y' + 3y = 0; y(0) = 1, y'(0) = 1/3

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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7. byty-zy= u 9. 4y"-4y' + y = 0 11. 4w" +20w' +25w = 0 12. 3y"+11y'-7y=0 10. y-y'-11 In Problems 13-20, solve the given initial value problem. 13. y" + 2y' -8y=0; y(0) =-3, y'(0) = -12 14. y"+y' = 0; y(0) = 2, y'(0) = 1 15. y"-4y+3y=0; y(0) = 1, y'(0) = 1/3 16. y"-4y'-5y = 0; y(-1) = 3, y'(-1)=9 17. y"-6y' +9y=0; y(0) = 2, y'(0) = 25/3 z(0) = 0. z'(0) = 3 18. 2"-22-2z = 0; 19. y" + 2y' +y=0; y(0) = 1, y'(0) = -3 20. y"-4y + 4y = 0; y(1) = 1, y'(1) = 1 21. First-Order Constant-Coefficient Equations. (a) Substituting y = e, find the auxiliary equation fa the first-order linear equation ay' + by = 0, where a and b are constants with a 0. (b) Use the result of part (a) to find the general solution In Problems 22-25, use the method described in Problem 2 to find a general solution to the given equation
Transcribed Image Text:7. byty-zy= u 9. 4y"-4y' + y = 0 11. 4w" +20w' +25w = 0 12. 3y"+11y'-7y=0 10. y-y'-11 In Problems 13-20, solve the given initial value problem. 13. y" + 2y' -8y=0; y(0) =-3, y'(0) = -12 14. y"+y' = 0; y(0) = 2, y'(0) = 1 15. y"-4y+3y=0; y(0) = 1, y'(0) = 1/3 16. y"-4y'-5y = 0; y(-1) = 3, y'(-1)=9 17. y"-6y' +9y=0; y(0) = 2, y'(0) = 25/3 z(0) = 0. z'(0) = 3 18. 2"-22-2z = 0; 19. y" + 2y' +y=0; y(0) = 1, y'(0) = -3 20. y"-4y + 4y = 0; y(1) = 1, y'(1) = 1 21. First-Order Constant-Coefficient Equations. (a) Substituting y = e, find the auxiliary equation fa the first-order linear equation ay' + by = 0, where a and b are constants with a 0. (b) Use the result of part (a) to find the general solution In Problems 22-25, use the method described in Problem 2 to find a general solution to the given equation
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