1. (a) If Z = [x f(2x + y) + g(2x + y)], where f and g are any arbitrary function, then find the partial differential equation of the given equation. (b) Form a partial differential equation of the family of spheres of radius 4 with centers on the yz -plane.
1. (a) If Z = [x f(2x + y) + g(2x + y)], where f and g are any arbitrary function, then find the partial differential equation of the given equation. (b) Form a partial differential equation of the family of spheres of radius 4 with centers on the yz -plane.
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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Please Answer all the questions.
![1. (a) If Z = [x f(2x + y) + g(2x + y)], where f and g are any arbitrary function,
then find the partial differential equation of the given equation.
(b) Form a partial differential equation of the family of spheres of radius 4 with
centers on the yz -plane.
Solve the following partial differential equations by using Lagrange's
method:
2.
i. O 9 =
y-z
x-y
p + ()
yz
zx
ху
ii.
(x² – y? – yz)p + (x² – y² – zx) q = z(x – y).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c9cd57c-5852-4698-b488-66c14101b682%2F506d2076-207f-4026-90a4-fff44ca9733a%2Fbrbv3g5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. (a) If Z = [x f(2x + y) + g(2x + y)], where f and g are any arbitrary function,
then find the partial differential equation of the given equation.
(b) Form a partial differential equation of the family of spheres of radius 4 with
centers on the yz -plane.
Solve the following partial differential equations by using Lagrange's
method:
2.
i. O 9 =
y-z
x-y
p + ()
yz
zx
ху
ii.
(x² – y? – yz)p + (x² – y² – zx) q = z(x – y).
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