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1. Consider the following partial differential equation: du ar2 (r, y) – 3(x, y) + 2u(x, y) = 0....(E). Let a and b be two real numbers. For which values of a and b, the function u(r, y) = f(y)eas + g(y)ebz is a solution of (E), where f(y), g(y) are two arbitrary functions. a) a = 2 and b= 3 b) a = 1 and b = 2 c) a = -2 and b = -1 d) None of the above,

1. Consider the following partial differential equation: du ar2 (r, y) – 3(x, y) + 2u(x, y) = 0....(E). Let a and b be two real numbers. For which values of a and b, the function u(r, y) = f(y)eas + g(y)ebz is a solution of (E), where f(y), g(y) are two arbitrary functions. a) a = 2 and b= 3 b) a = 1 and b = 2 c) a = -2 and b = -1 d) None of the above,

Advanced Engineering Mathematics
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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1. Consider the following partial differential equation: du (T,y) -3 (r, y) + 2u(r, y) = 0....(E). Let a and b be two real numbers. For which values of a and b, the function u(x, y) = f(y)ear + g(y)eb" is a solution of (E), where f(y), g(y) are two arbitrary functions. a) a = 2 and b = 3 b) a = 1 and b= 2 c) a = -2 and b = -1 d) None of the above. 2. Using the characteristic method, the solution of the following partial differential equation: |ru + (y+1)uy = u |u(x,0) = f(x), %3D where f is a given function. a) u(r, y) = (y + 1)f ( b) u(x, y) = (y² + 1)f( ). c) u(r, y) = f() d) None of the above. 3. The partial differential equation uz.Urr+ Urr.Uyy – u -r = 0 is a) Second order quasi-linear non-homogenous equation. b) Second order quasi-linear homogenous equation. c) Second order homogenous linear equation. d) None of the above.
Transcribed Image Text:1. Consider the following partial differential equation: du (T,y) -3 (r, y) + 2u(r, y) = 0....(E). Let a and b be two real numbers. For which values of a and b, the function u(x, y) = f(y)ear + g(y)eb" is a solution of (E), where f(y), g(y) are two arbitrary functions. a) a = 2 and b = 3 b) a = 1 and b= 2 c) a = -2 and b = -1 d) None of the above. 2. Using the characteristic method, the solution of the following partial differential equation: |ru + (y+1)uy = u |u(x,0) = f(x), %3D where f is a given function. a) u(r, y) = (y + 1)f ( b) u(x, y) = (y² + 1)f( ). c) u(r, y) = f() d) None of the above. 3. The partial differential equation uz.Urr+ Urr.Uyy – u -r = 0 is a) Second order quasi-linear non-homogenous equation. b) Second order quasi-linear homogenous equation. c) Second order homogenous linear equation. d) None of the above.
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