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In Exercises 1-6, find the general solution of the equation specified. dy =-4y+9e¹ 2. =-4y+3e dt 1. 3. dt 7. dt 5. d=3y-4e² 9. =-3y + 4 cos2r dt dt In Exercises 7-12, solve the given initial-value problem. +2y=e, y(0)=1 +y=cos 2r, -2y=7e². 4. y(0) = 5 y(0) = 3 dt = 2y + sin2r -2y=3e²y(0) = 10 10. +3y=cos 21, y(0)=-1 dt dt 12.-2y=7e", y(0) = 3 dt

In Exercises 1-6, find the general solution of the equation specified. dy =-4y+9e¹ 2. =-4y+3e dt 1. 3. dt 7. dt 5. d=3y-4e² 9. =-3y + 4 cos2r dt dt In Exercises 7-12, solve the given initial-value problem. +2y=e, y(0)=1 +y=cos 2r, -2y=7e². 4. y(0) = 5 y(0) = 3 dt = 2y + sin2r -2y=3e²y(0) = 10 10. +3y=cos 21, y(0)=-1 dt dt 12.-2y=7e", y(0) = 3 dt

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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In Exercises 1-6, find the general solution of the equation specified. dy -4y +9e-¹ dt 1. dt dy 3. = -3y + 4 cos 2t dt 5. 9. dy dt 11. dy dt = 3y -4e³t dy dt + y = cos 2t, y (0) = 5 2. In Exercises 7-12, solve the given initial-value problem. dy dy 7. +2y=e¹/3, y(0) = 1 dt dt - 2y = 7e²t, y(0) = = 3 4. 6. 8. dy dt 12. -4y+3e-t = 2y + sin 2t dy y dt 2 dy dt +4e¹/2 dy 10. +3y= = cos 2t, y(0) = -1 dt - 2y = 3e=²¹, y(0) = 10 - 2y = 7e²t, y (0)= 3
Transcribed Image Text:In Exercises 1-6, find the general solution of the equation specified. dy -4y +9e-¹ dt 1. dt dy 3. = -3y + 4 cos 2t dt 5. 9. dy dt 11. dy dt = 3y -4e³t dy dt + y = cos 2t, y (0) = 5 2. In Exercises 7-12, solve the given initial-value problem. dy dy 7. +2y=e¹/3, y(0) = 1 dt dt - 2y = 7e²t, y(0) = = 3 4. 6. 8. dy dt 12. -4y+3e-t = 2y + sin 2t dy y dt 2 dy dt +4e¹/2 dy 10. +3y= = cos 2t, y(0) = -1 dt - 2y = 3e=²¹, y(0) = 10 - 2y = 7e²t, y (0)= 3
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