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4) a²u/ x² = 1/ 16 a2u/ at² over 0 0 for the boundary conditions u(0, t) = 0.0, u(2,t) + du/dx(2,t) = 0 the initial conditions du/dt(x,0) = 0 and u(x, 0) = 6 sin лx 5) 0²u/ x² = 1/ 16 a2u/ at² over 0 0 for the boundary conditions u(0, t) = 7.0, u(2,t) + du/dx(2,t) == 0 the initial conditions du/dt(x,0) = 0 and u(x, 0) = 6 sin лx 6) a²u/ ax² + 1/ 16 a2u/ ay2 = 0over 0

4) a²u/ x² = 1/ 16 a2u/ at² over 0 0 for the boundary conditions u(0, t) = 0.0, u(2,t) + du/dx(2,t) = 0 the initial conditions du/dt(x,0) = 0 and u(x, 0) = 6 sin лx 5) 0²u/ x² = 1/ 16 a2u/ at² over 0 0 for the boundary conditions u(0, t) = 7.0, u(2,t) + du/dx(2,t) == 0 the initial conditions du/dt(x,0) = 0 and u(x, 0) = 6 sin лx 6) a²u/ ax² + 1/ 16 a2u/ ay2 = 0over 0

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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I want the sol of this equation using the separation of vairables

4) a²u/ x² = 1/ 16 au/ at² over 0 <x< 2, t> 0 for the boundary conditions u(0, t) = 0.0, u(2,t) + du/dx(2,t) = 0 the initial conditions du/dt(x,0) = 0 and u(x, 0) = 6 sin èx 5) a²u/ x² = 1/ 16 a²u/ at² over 0 <x< 2, t> 0 for the boundary conditions u(0, t) = 7.0, u(2,t) + du/dx(2,t) —= 0 the initial conditions du/dt(x,0) = 0 and u(x, 0) = 6 sin èx 6) a²u/ x² + 1/ 16 №²u/ Əy² = 0over 0 <x< 2, 0 <y< 3 for the boundary conditions u(0, y) = 0.0, u(2,y)=0 the initial conditions du/dy(x,0) = 0 and u(x, 0) = 6 sin éx 7) a²u/ x² + x +1/ 16 ởu/ ôy² = 0over 0 <x< 2, 0 <y< 3 for the boundary conditions u(0, y) = 0.0, u(2,y) = 0 the initial conditions du/dy(x,0) = 0 and u(x, 0) = 6 sin èx 8) a²u/ x² + 1/ 16 2u/ Əy² = 0 over 0 <x< 2, 0 <y< 3 for the boundary conditions u(0, y) = y², u(2,y) = 0 the initial conditions du/dy(x,0) = 0 and u(x, 0) = 6 sin éx I
Transcribed Image Text:4) a²u/ x² = 1/ 16 au/ at² over 0 <x< 2, t> 0 for the boundary conditions u(0, t) = 0.0, u(2,t) + du/dx(2,t) = 0 the initial conditions du/dt(x,0) = 0 and u(x, 0) = 6 sin èx 5) a²u/ x² = 1/ 16 a²u/ at² over 0 <x< 2, t> 0 for the boundary conditions u(0, t) = 7.0, u(2,t) + du/dx(2,t) —= 0 the initial conditions du/dt(x,0) = 0 and u(x, 0) = 6 sin èx 6) a²u/ x² + 1/ 16 №²u/ Əy² = 0over 0 <x< 2, 0 <y< 3 for the boundary conditions u(0, y) = 0.0, u(2,y)=0 the initial conditions du/dy(x,0) = 0 and u(x, 0) = 6 sin éx 7) a²u/ x² + x +1/ 16 ởu/ ôy² = 0over 0 <x< 2, 0 <y< 3 for the boundary conditions u(0, y) = 0.0, u(2,y) = 0 the initial conditions du/dy(x,0) = 0 and u(x, 0) = 6 sin èx 8) a²u/ x² + 1/ 16 2u/ Əy² = 0 over 0 <x< 2, 0 <y< 3 for the boundary conditions u(0, y) = y², u(2,y) = 0 the initial conditions du/dy(x,0) = 0 and u(x, 0) = 6 sin éx I
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