respect to x. ng sides of Supplementary Problems Use variation of parameters to find the general solutions of the following differential equations: 12.9.) y" - 2y' + y = et 12.10. y" +y= sec x 12.11. y" -y'- 2y = e3* 12.12. y" – 60y' – 900y = 5e10x %3D 12.13.) y"- 7y' =- 3 12.14. y"+y- y = In x if two solutions to the associated homogeneous problem are known to be x and 17x. 12.15. xy"- xy' x'e* if two solutions to the associated homogeneous problem are known to be 1 and x". (1) 12.16. y--y=x² and v =x19. y +2xy = x 12.17. %3D e' * - 2x + x =- 12.18. y" = 12 %3D 12.19. 12.20. й — 6х +9х: *+ 4x = 4 sec? 2t 12.21. e' * - 4x + 3x = 12.22. %3D 1+e' (t – 1)ä – 2tx + 2x = (t – 1) if two solutions to the associated homogeneous equations are known to be t and + 1. 12.23. %3D (t2 +t)ï + (2 – t²)x – (2 +t)x =t(t+1)² if two solutions to the associated homogeneous equations are known to be 12.24. e' and 1/t. (1) e' 12.25.) - 3ii + 3r -r =- ř + 6ř +12r + 8r = 12e2 12.26. %3D d'z 3 e30 dz +2- de 1+ e° 12.28. - 52 + 25ż – 125z = 1000 %3D 12.27. d0² do3 12.29. t°ÿ + 3t²j = 1 if three linearly independent solutions to the associated homogeneous equations are known to be 1/t, 1, and t. y(5) – 4y(3) = 32e2r 12.30. %3D /2
respect to x. ng sides of Supplementary Problems Use variation of parameters to find the general solutions of the following differential equations: 12.9.) y" - 2y' + y = et 12.10. y" +y= sec x 12.11. y" -y'- 2y = e3* 12.12. y" – 60y' – 900y = 5e10x %3D 12.13.) y"- 7y' =- 3 12.14. y"+y- y = In x if two solutions to the associated homogeneous problem are known to be x and 17x. 12.15. xy"- xy' x'e* if two solutions to the associated homogeneous problem are known to be 1 and x". (1) 12.16. y--y=x² and v =x19. y +2xy = x 12.17. %3D e' * - 2x + x =- 12.18. y" = 12 %3D 12.19. 12.20. й — 6х +9х: *+ 4x = 4 sec? 2t 12.21. e' * - 4x + 3x = 12.22. %3D 1+e' (t – 1)ä – 2tx + 2x = (t – 1) if two solutions to the associated homogeneous equations are known to be t and + 1. 12.23. %3D (t2 +t)ï + (2 – t²)x – (2 +t)x =t(t+1)² if two solutions to the associated homogeneous equations are known to be 12.24. e' and 1/t. (1) e' 12.25.) - 3ii + 3r -r =- ř + 6ř +12r + 8r = 12e2 12.26. %3D d'z 3 e30 dz +2- de 1+ e° 12.28. - 52 + 25ż – 125z = 1000 %3D 12.27. d0² do3 12.29. t°ÿ + 3t²j = 1 if three linearly independent solutions to the associated homogeneous equations are known to be 1/t, 1, and t. y(5) – 4y(3) = 32e2r 12.30. %3D /2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Question #12.13 from the image. Differential Equations
Transcribed Image Text:respect to x.
ng
sides of
Supplementary Problems
Use variation of parameters to find the general solutions of the following differential equations:
12.9.) y" - 2y' + y =
et
12.10.
y" +y= sec x
12.11. y" -y'- 2y = e3*
12.12.
y" – 60y' – 900y = 5e10x
%3D
12.13.) y"- 7y' =- 3
12.14. y"+y-
y = In x if two solutions to the associated homogeneous problem are known to be x and 17x.
12.15.
xy"- xy' x'e* if two solutions to the associated homogeneous problem are known to be 1 and x".
(1)
12.16. y--y=x²
and v =x19.
y +2xy = x
12.17.
%3D
e'
* - 2x + x =-
12.18. y" = 12
%3D
12.19.
12.20.
й — 6х +9х:
*+ 4x = 4 sec? 2t
12.21.
e'
* - 4x + 3x =
12.22.
%3D
1+e'
(t – 1)ä – 2tx + 2x = (t – 1) if two solutions to the associated homogeneous equations are known to be t and + 1.
12.23.
%3D
(t2 +t)ï + (2 – t²)x – (2 +t)x =t(t+1)² if two solutions to the associated homogeneous equations are known to be
12.24.
e' and 1/t.
(1)
e'
12.25.) - 3ii + 3r -r =-
ř + 6ř +12r + 8r = 12e2
12.26.
%3D
d'z
3
e30
dz
+2-
de 1+ e°
12.28.
- 52 + 25ż – 125z = 1000
%3D
12.27.
d0²
do3
12.29. t°ÿ + 3t²j = 1 if three linearly independent solutions to the associated homogeneous equations are known to be
1/t, 1, and t.
y(5) – 4y(3) = 32e2r
12.30.
%3D
/2
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