Problem 1) part (A): 1: Find the 2x- periodic solution u(t, x) to дти = Чихх u (0,x) = 5 cos (3x) - 2 sin (2x) +4 part (B): Find the solution u(t, x) to ди= бихх u(€, 0) = u(t, 10)=0 t> 0, XER XERR u(0,x) = -2 sin ( 3xx ) + b sin (5TX) + 5 sin ( 6xx) 10 : part (C) Find the solution u(t,x) to 764 = 24xx ux (t, 0) = ux (t, 1) = 0 u (o, x ) = -2 + 4 cs (TX) - 765 (12xx) t70, 06x-10 t>o 00, 0

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 18E: Find the general solution for each differential equation. Verify that each solution satisfies the...
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Can you show how exactly to solve these using separation of variables and Fourier Series?
Problem 1)
part (A):
1: Find the 2x- periodic solution u(t, x) to
дти = Чихх
u (0,x) = 5 cos (3x) - 2 sin (2x) +4
part (B): Find the solution u(t, x) to
ди= бихх
u(€, 0) = u(t, 10)=0
t> 0, XER
XERR
u(0,x) = -2 sin ( 3xx ) + b sin (5TX) + 5 sin ( 6xx)
10
:
part (C) Find the solution u(t,x) to
764 = 24xx
ux (t, 0) = ux (t, 1) = 0
u (o, x ) = -2 + 4 cs (TX) - 765 (12xx)
t70, 06x-10
t>o
0<x<10
t>0, 0<x<1
t7o
Transcribed Image Text:Problem 1) part (A): 1: Find the 2x- periodic solution u(t, x) to дти = Чихх u (0,x) = 5 cos (3x) - 2 sin (2x) +4 part (B): Find the solution u(t, x) to ди= бихх u(€, 0) = u(t, 10)=0 t> 0, XER XERR u(0,x) = -2 sin ( 3xx ) + b sin (5TX) + 5 sin ( 6xx) 10 : part (C) Find the solution u(t,x) to 764 = 24xx ux (t, 0) = ux (t, 1) = 0 u (o, x ) = -2 + 4 cs (TX) - 765 (12xx) t70, 06x-10 t>o 0<x<10 t>0, 0<x<1 t7o
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,