1. Classify the following differential equations as to ODE/PDE, order, degree, linearity, coefficients type and homogeneity. State the independent variables and unknown functions. [you can use a table] 1. y+rx) 0. 6. dx 7. dt + = 1, dy %3D dt 8. Σa (x) a@y f(x), where dx° d°y = y, %3D0 + xz" - yz = 0 3xy' y - z' + y" = 0 10. (1 - x)y'- 4xy = cos x, d²y 9. 4 11. x dx2 + 4y = 0, dx 12. t*y(5) - ty" + 6y = 0, d?u 13. dr2 du +u cos(r + 1), dr d²y 些=1+() dy 14. %3D dx2 dx, 15. uxx + Uyy = 0, d?R 16. dt2 k %3D R2' 17. (sin 0)y" – (cos 0)y' = 2 exp(y), 18. * - (1-)i +x = 0.
1. Classify the following differential equations as to ODE/PDE, order, degree, linearity, coefficients type and homogeneity. State the independent variables and unknown functions. [you can use a table] 1. y+rx) 0. 6. dx 7. dt + = 1, dy %3D dt 8. Σa (x) a@y f(x), where dx° d°y = y, %3D0 + xz" - yz = 0 3xy' y - z' + y" = 0 10. (1 - x)y'- 4xy = cos x, d²y 9. 4 11. x dx2 + 4y = 0, dx 12. t*y(5) - ty" + 6y = 0, d?u 13. dr2 du +u cos(r + 1), dr d²y 些=1+() dy 14. %3D dx2 dx, 15. uxx + Uyy = 0, d?R 16. dt2 k %3D R2' 17. (sin 0)y" – (cos 0)y' = 2 exp(y), 18. * - (1-)i +x = 0.
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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Question
![1. Classify the following differential equations as to ODE/PDE, order, degree, linearity,
coefficients type and homogeneity. State the independent variables and unknown functions.
[you can use a table]
. y+P)-
--U.
= se
0.
6.
dx
7. *+ dy
= 1,
dt
dt
8. E-o a (x) a®y
[3xy' + xz" - yz = 0
y - z'+ y" = 0
dx=f(x), where
dx0
d°y
= y,
9.
%3D
10. (1 – x)y' - 4xy = cos x,
d²y
11. x
dx2
dy
+ 4y = 0,
12. t*y(5) - ty" + 6y = 0,
d?u
13.
dr2
du
+u cos(r + 1),
dr
d?y
14.
dx2
1+
%3D
15. uxx + Uyy
= 0,
d?R
16.
dt2
k
R2
17. (sin 0)y" – (cos 0)y' = 2 exp(y),
(1-)i +x = 0.
%3D
18. * -
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1bd5ecff-7eab-4c0b-b769-61204093d9be%2F6ac60610-245d-4d0c-89f6-b5f610e062d9%2Fvjcto79_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Classify the following differential equations as to ODE/PDE, order, degree, linearity,
coefficients type and homogeneity. State the independent variables and unknown functions.
[you can use a table]
. y+P)-
--U.
= se
0.
6.
dx
7. *+ dy
= 1,
dt
dt
8. E-o a (x) a®y
[3xy' + xz" - yz = 0
y - z'+ y" = 0
dx=f(x), where
dx0
d°y
= y,
9.
%3D
10. (1 – x)y' - 4xy = cos x,
d²y
11. x
dx2
dy
+ 4y = 0,
12. t*y(5) - ty" + 6y = 0,
d?u
13.
dr2
du
+u cos(r + 1),
dr
d?y
14.
dx2
1+
%3D
15. uxx + Uyy
= 0,
d?R
16.
dt2
k
R2
17. (sin 0)y" – (cos 0)y' = 2 exp(y),
(1-)i +x = 0.
%3D
18. * -
1
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