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In Exercises 7-12, solve the given initial-value problem. dy +2, y(0) = 3 8. = dt 7. dy dt 11. dy 9. = dt dy dt t 13. dy 10. = -2ty +4e-¹², y(0) = 3 dt y=2t³e²¹₁_y(1) = 0 In Exercises 13-18, the differential equation is linear, and in theory, we can find its general solution using the method of integrating factors. However, since this method involves computing two integrals, in practice it is frequently impossible to reach a for- mula for the solution that is free of integrals. For these exercises, determine the general solution to the equation and express it with as few integrals as possible. dy dt dy dt - 1+1 15. = dy 17. = dt y = (sint)y +4 +2, y(1) = 3 2y = 2t², y(-2) = 4 y 1² + 4 cost y et2 + cost 12. dy dt dy dt 16. - dy dt 14. d = 1²y +4 dy dt 1 +1 3 t dy 18. = dt -y+4t² +4t, y(1) = 10 = y + 4 cost² = aty +4e-t²? y 13-3 19. For what value(s) of the parameter a is it possible to find explicit formulas (without integrals) for the solutions to +t

In Exercises 7-12, solve the given initial-value problem. dy +2, y(0) = 3 8. = dt 7. dy dt 11. dy 9. = dt dy dt t 13. dy 10. = -2ty +4e-¹², y(0) = 3 dt y=2t³e²¹₁_y(1) = 0 In Exercises 13-18, the differential equation is linear, and in theory, we can find its general solution using the method of integrating factors. However, since this method involves computing two integrals, in practice it is frequently impossible to reach a for- mula for the solution that is free of integrals. For these exercises, determine the general solution to the equation and express it with as few integrals as possible. dy dt dy dt - 1+1 15. = dy 17. = dt y = (sint)y +4 +2, y(1) = 3 2y = 2t², y(-2) = 4 y 1² + 4 cost y et2 + cost 12. dy dt dy dt 16. - dy dt 14. d = 1²y +4 dy dt 1 +1 3 t dy 18. = dt -y+4t² +4t, y(1) = 10 = y + 4 cost² = aty +4e-t²? y 13-3 19. For what value(s) of the parameter a is it possible to find explicit formulas (without integrals) for the solutions to +t

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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HELP ASAP! #7 & #13
In Exercises 7-12, solve the given initial-value problem. +2, y(0) = 3 dy 1 dt t+1 7. 9. == dt 11. 13. dy dt 15. 17. dy 2y dt t dy dt 1+t dy dt y t dy dt In Exercises 13-18, the differential equation is linear, and in theory, we can find its general solution using the method of integrating factors. However, since this method involves computing two integrals, in practice it is frequently impossible to reach a for- mula for the solution that is free of integrals. For these exercises, determine the general solution to the equation and express it with as few integrals as possible. = 2t², y(-2) = 4 y 12 -2, y(1) = 3 = (sint)y +4 + 4 cost y e12 + cost 8. = dy dt 10. = dt y (0) = 3 3 12. - ²y = 21³e²¹, y(1) = 0 dy dt t 16. dy 14. =t²y +4 dt dy dt y+4t² + 4t, y(1) = 10 -2ty +4e-1², dy 18. = dt = y + 4 cost² = aty +4e-t²? 19. For what value(s) of the parameter a is it possible to find explicit formulas (without integrals) for the solutions to dy = t'y +4? dt y 13-3 +t 20. For what value(s) of the parameter r is it possible to find explicit formulas (without integrals) for the solutions to Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). tent does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
Transcribed Image Text:In Exercises 7-12, solve the given initial-value problem. +2, y(0) = 3 dy 1 dt t+1 7. 9. == dt 11. 13. dy dt 15. 17. dy 2y dt t dy dt 1+t dy dt y t dy dt In Exercises 13-18, the differential equation is linear, and in theory, we can find its general solution using the method of integrating factors. However, since this method involves computing two integrals, in practice it is frequently impossible to reach a for- mula for the solution that is free of integrals. For these exercises, determine the general solution to the equation and express it with as few integrals as possible. = 2t², y(-2) = 4 y 12 -2, y(1) = 3 = (sint)y +4 + 4 cost y e12 + cost 8. = dy dt 10. = dt y (0) = 3 3 12. - ²y = 21³e²¹, y(1) = 0 dy dt t 16. dy 14. =t²y +4 dt dy dt y+4t² + 4t, y(1) = 10 -2ty +4e-1², dy 18. = dt = y + 4 cost² = aty +4e-t²? 19. For what value(s) of the parameter a is it possible to find explicit formulas (without integrals) for the solutions to dy = t'y +4? dt y 13-3 +t 20. For what value(s) of the parameter r is it possible to find explicit formulas (without integrals) for the solutions to Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). tent does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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