Use the method for solving equations with linear coefficients to solve the following differential equation. (2x-y) dx + (4x + y-3) dy = 0 Express the related system in terms of h and k. Choose the correct answer below. O A O B. OC. O D. dv du - 2h - k = 0 - 4h+k=3 2h-k=0 4h+k = 3 dz 2h + 2k = 0 - h+k=3 Find the differential equation 2h - k = x 4h + k = y dv du in terms of v and u. V Let z = Find the differential equation dz du *
Use the method for solving equations with linear coefficients to solve the following differential equation. (2x-y) dx + (4x + y-3) dy = 0 Express the related system in terms of h and k. Choose the correct answer below. O A O B. OC. O D. dv du - 2h - k = 0 - 4h+k=3 2h-k=0 4h+k = 3 dz 2h + 2k = 0 - h+k=3 Find the differential equation 2h - k = x 4h + k = y dv du in terms of v and u. V Let z = Find the differential equation dz du *
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
Clarification needed
Ignoring lost solutions if May am implicit solution in terms of u and z is ________ = C, where C is an arbitrary constant.
Using back substitution , an implicit solution in the form F(x,y) = C is _______ = C , where C is an arbitrary constant. (Type an expres
![Step 1:
(2x − y) dx + (4x + y − 3) d y = 0
Let x = u+h, y=v+k
2x - Y
= 2u + 2h - v -k (a
4x + y − 3
⇒ 4u +4h+v+k-3
.. (2x − y) dx + (4x + y − 3) dy=0
⇒ (2uv + 2h - k) du + (4u+v+4h+k-3) dv=0
-
Now let 2h - k = 0, 4h + k − 3 = 0
Hence option (B) is correct
(2u - v) du + (4u + v) dv=0
Since 2h — k = 0, 4h + k − 3 = 0
v-2u
v+4u
dv
du
=
dv
Hence =
du
Step 2:
Let z =
dz
du
=
=
=
Hence
v-2u
v+4u
V
U
υ
21,²
+
u²
dz
du
zu
u²
z-2
u(z+4)
1 dv
u du
==
+
2-2
U z+4
+
ՂԱ
1 v-2u
u v+4u
1
zu-2u
U zu+4u
N|3
[22-2]
z+4
[···z = 2/201
Ա](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F855e3b16-f6f3-4bd4-8eb4-9b636bc369c1%2F047bad67-e9d3-477a-89ab-a4b441d60742%2Fnu6o13b8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Step 1:
(2x − y) dx + (4x + y − 3) d y = 0
Let x = u+h, y=v+k
2x - Y
= 2u + 2h - v -k (a
4x + y − 3
⇒ 4u +4h+v+k-3
.. (2x − y) dx + (4x + y − 3) dy=0
⇒ (2uv + 2h - k) du + (4u+v+4h+k-3) dv=0
-
Now let 2h - k = 0, 4h + k − 3 = 0
Hence option (B) is correct
(2u - v) du + (4u + v) dv=0
Since 2h — k = 0, 4h + k − 3 = 0
v-2u
v+4u
dv
du
=
dv
Hence =
du
Step 2:
Let z =
dz
du
=
=
=
Hence
v-2u
v+4u
V
U
υ
21,²
+
u²
dz
du
zu
u²
z-2
u(z+4)
1 dv
u du
==
+
2-2
U z+4
+
ՂԱ
1 v-2u
u v+4u
1
zu-2u
U zu+4u
N|3
[22-2]
z+4
[···z = 2/201
Ա
![Use the method for solving equations with linear coefficients to solve the following differential equation.
(2x - y) dx + (4x+y-3) dy=0
Express the related system in terms of h and k. Choose the correct answer below.
O A.
O B.
O C.
O D.
dv
du
-2h-k=0
- 4h+k=3
2h-k=0
4h+k=3
dz
du
2h+2k=0
-h+k=3
Find the differential equation
2h-k=x
4h+k=y
dv
du
in terms of v and u.
V
Let z = . Find the differential equation
u
dz
du
]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F855e3b16-f6f3-4bd4-8eb4-9b636bc369c1%2F047bad67-e9d3-477a-89ab-a4b441d60742%2F1y4yax_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use the method for solving equations with linear coefficients to solve the following differential equation.
(2x - y) dx + (4x+y-3) dy=0
Express the related system in terms of h and k. Choose the correct answer below.
O A.
O B.
O C.
O D.
dv
du
-2h-k=0
- 4h+k=3
2h-k=0
4h+k=3
dz
du
2h+2k=0
-h+k=3
Find the differential equation
2h-k=x
4h+k=y
dv
du
in terms of v and u.
V
Let z = . Find the differential equation
u
dz
du
]
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