Suppose that the C2 function z = f(x, y) satisfies the differential equation 8²% 8²% 8²% +c- = 0 əxəy dy² 0x² a +26. Page 1 of 2 where a, b, c are nonzero real numbers such that b²-ac=0. Show that if we let x = and yt, then z satisfies the simpler equation Ət² for some constant a. Determine a explicitly. = α T
Suppose that the C2 function z = f(x, y) satisfies the differential equation 8²% 8²% 8²% +c- = 0 əxəy dy² 0x² a +26. Page 1 of 2 where a, b, c are nonzero real numbers such that b²-ac=0. Show that if we let x = and yt, then z satisfies the simpler equation Ət² for some constant a. Determine a explicitly. = α T
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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![Q3. Suppose that the C2 function z = f(x, y) satisfies the differential equation
+ 26
+ c
= 0
Əx²
dxdy
Page 1 of 2
where a, b, c are nonzero real numbers such that b2 – ac = 0. Show that if we let x =
b
and y = t, then z satisfies the simpler equation
for some constant a. Determine a explicitly.
(Note: Using this, we can now easily find all functions that satisfy the original differential
equation. Do you see how? (This is not part of the assignment and does not need to be
submitted.)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0db73129-ae61-4d51-93c4-ffd44dc3dc9a%2F1bf9ccec-7b4a-4b75-9bac-e5ed5bfc03dd%2Fkpux5yl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q3. Suppose that the C2 function z = f(x, y) satisfies the differential equation
+ 26
+ c
= 0
Əx²
dxdy
Page 1 of 2
where a, b, c are nonzero real numbers such that b2 – ac = 0. Show that if we let x =
b
and y = t, then z satisfies the simpler equation
for some constant a. Determine a explicitly.
(Note: Using this, we can now easily find all functions that satisfy the original differential
equation. Do you see how? (This is not part of the assignment and does not need to be
submitted.)]
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