1. Classify the following differential equations as to ODE/PDE, order, degree, linearity, coefficients type and homogeneity. State the independent variables and unknown functions. lyou can use a table] 1. ý + P(x)y = Q(x), 3 + 6x = 0, dx2 dx 3. (9 + 5s*t3 = se2s,
1. Classify the following differential equations as to ODE/PDE, order, degree, linearity, coefficients type and homogeneity. State the independent variables and unknown functions. lyou can use a table] 1. ý + P(x)y = Q(x), 3 + 6x = 0, dx2 dx 3. (9 + 5s*t3 = se2s,
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]
1. ý + P(x)y = Q(x),
2. 4 4?y
+ 3 + 6x = 0,
dx2
dx
3. ( + 5s*t3 = se2s,
dt3
a?u(x.y)
azu(x.y)
ду?
4.
= 0,
ax2
3
5. + 1 = ( - x²,
[d²x
%3D
dt2
dt
dx
6.
dy
+ y2x sin y,
dx
7.
dt
dy
= 1,
dt
d@y
d°y
8. E-0 a;(x) = f(x), where
= y
dx°
$3xy' + xz"- yz = 0
9.
y - z' + y" = 0
10. (1 – x)y' – 4xy = cos x,
a²y
4
dy
) + 4y = 0,
12. t*y(5)- ty'" + 6y = 0,
11. x
dx2
dx
%3D
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 8)y' = 2 exp(y),
(1-)* + x = 0.
18. * -](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b196659-560e-4d50-9755-32d5047f2e0c%2Fb6387b9e-f01b-425f-979b-d1fd506a17bd%2Fe6vlvfb_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]
1. ý + P(x)y = Q(x),
2. 4 4?y
+ 3 + 6x = 0,
dx2
dx
3. ( + 5s*t3 = se2s,
dt3
a?u(x.y)
azu(x.y)
ду?
4.
= 0,
ax2
3
5. + 1 = ( - x²,
[d²x
%3D
dt2
dt
dx
6.
dy
+ y2x sin y,
dx
7.
dt
dy
= 1,
dt
d@y
d°y
8. E-0 a;(x) = f(x), where
= y
dx°
$3xy' + xz"- yz = 0
9.
y - z' + y" = 0
10. (1 – x)y' – 4xy = cos x,
a²y
4
dy
) + 4y = 0,
12. t*y(5)- ty'" + 6y = 0,
11. x
dx2
dx
%3D
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 8)y' = 2 exp(y),
(1-)* + x = 0.
18. * -
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