Consider the following partial differential equation: y(e + 1)u, – e"(y² + 1)²u, = 0, y > 0 (F) 1. By using the separation method with u(r, y) = f(r)+g(y) to solve (F), we obtain that : (y² + 1)² dg dy (y² + 1)² dg dy dg 1+e df a) dr et b) 1+ e dr df 1+e" df c) e dr (y? + 1)2 dy d) None of the above. 2. A solution u(r, y) of (F) is ( B is an arbitrary constant): a) u(r, y) = A (In(1+e*) – In(y² +1)) + B. 1 b) u(r, y) = 1(In(1 + e)- + B. 2(y² + 1). %3D + B. 2(y? + 1) d) None af the above.
Consider the following partial differential equation: y(e + 1)u, – e"(y² + 1)²u, = 0, y > 0 (F) 1. By using the separation method with u(r, y) = f(r)+g(y) to solve (F), we obtain that : (y² + 1)² dg dy (y² + 1)² dg dy dg 1+e df a) dr et b) 1+ e dr df 1+e" df c) e dr (y? + 1)2 dy d) None of the above. 2. A solution u(r, y) of (F) is ( B is an arbitrary constant): a) u(r, y) = A (In(1+e*) – In(y² +1)) + B. 1 b) u(r, y) = 1(In(1 + e)- + B. 2(y² + 1). %3D + B. 2(y? + 1) d) None af the above.
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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Transcribed Image Text:Consider the following partial differential equation:
y(e +1)u, – e"(y² + 1)²u, = 0, y >0
1. By using the separation method with u(r, y) = f(r)+ g(y) to solve (F), we obtain that :
(F)
1+ e" df
(y² + 1)² dg
a)
da
fip
df
b)
1+ er dr
(y? + 1)? dg
dy
dg
et
%3D
1+ e" df
c)
et
dr
(y? +1)2 dy
d) None of the above.
2. A solution u(x, y) of (F) is ( B is an arbitrary constant):
a) u(r, y) = À (In(1+ e*) – In(y² +1)) + B.
1
b) u(x, y) = (In(1 + e")-
+ B.
2(y² + 1)
1
c) u(r, y) = A
+ B.
2(y? + 1).
d) None af the above.
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