ONLY ANSWER 5 and 9. Rating will be provided Exercises for Section 6.2 In Exercises 1-12 use the separation of variables method to solve the heat equation (a, t)auz(t<<l,t>0, subject t...

Question

Question

ONLY ANSWER 5 and 9. Rating will be provided

Answer 1

Answer #1

ant, tant レn.se Rns aulindafurdant-og auh omos Smu am Care λ=0 So, 12 ne n 교 而;itn.uadd 02 02 댜 2- C 2. 20+ -2- (ant) an+リ 니 21-t

Answer 2

Similar Homework Help Questions

Solve the heat equation by the method of separation of variables 1(1, t) = 0 Эт u,(0, t) = 0, u(x,0) =-2cos( 12. Solve the heat equation by the method of separation of variables 1(1, t) = 0 Эт u...

Solve the heat equation by the method of separation of variables 1(1, t) = 0 Эт u,(0, t) = 0, u(x,0) =-2cos( 12. Solve the heat equation by the method of separation of variables 1(1, t) = 0 Эт u,(0, t) = 0, u(x,0) =-2cos( 12.
3. Using separation of variables to solve the heat equation, u -kuxx on the interval 0x<1...

3. Using separation of variables to solve the heat equation, u -kuxx on the interval 0x<1 with boundary conditions u(0 and ur(1, t)-0, yields the general solution, u(x, t) =A0 + Σ Ane-k,t cos(nm) (with A, = ㎡π2) 0<x<l/2 0〈x〈1,2 u(x,0)=f(x)-.., , . . .) when u(x,0) = f(x)- Determine the coefficients An (n - 0, 1,2,
3. Using separation of variables to solve the heat equation, u- kuxx on the interval 0 < x< 1 with boundary conditions ux(0, t) = 0 and ux(1, t) yields the general solution, 1, 0<x < 1/2...

3. Using separation of variables to solve the heat equation, u- kuxx on the interval 0 < x< 1 with boundary conditions ux(0, t) = 0 and ux(1, t) yields the general solution, 1, 0<x < 1/2 0, 1/2 x<1 Determine the coefficients An (n = 0, 1, 2, . . .) when u(x,0) = f(x) = 3. Using separation of variables to solve the heat equation, u- kuxx on the interval 0

a) Use the d'Alembert solution to solve au au - <r< ,t> 0, at2 48,2 ux,0)...

a) Use the d'Alembert solution to solve au au - <r< ,t> 0, at2 48,2 ux,0) = cos 3x, u(,0) = 21 b) Consider the heat equation диди 0<x<1, t > 0, at ax? with boundary conditions uz (0,t) = 0, uz(1,t) = 0, > 0, and initial conditions u(x,0) = { 0, 2.0, 0<r < 0.5, 0.5 <<1. Use the method of separation of variables to solve the equation.
(a) Use separation of variables to rewrite the partial differential equation below into a pair 1....

(a) Use separation of variables to rewrite the partial differential equation below into a pair 1. of ordinary differential equations. (b) Suppose the above partial differential equation has boundary condition uz (0,t) 0, u(20, t)0. Use separations of variables to determine the corresponding bound- ary conditions that the ordinary differential equations found in (a) must satisfy. (c) (Yes or no) Could the partial differential equation, u -2uzt-5utt, be separated into two ordinary differential equations? (a) Use separation of variables to...
1. Solve the following transient heat equation by separation of variable method. ат ах Atx=L, T =To IC: At t = 0, T=T,...

1. Solve the following transient heat equation by separation of variable method. ат ах Atx=L, T =To IC: At t = 0, T=T, 1. Solve the following transient heat equation by separation of variable method. ат ах Atx=L, T =To IC: At t = 0, T=T,

1. Solve the following transient heat equation by separation of variable method. aT At x = 0, BC み_Qo Atx=L, T =To IC: At t = 0, T= 1. Solve the following transient heat equation by separat...

1. Solve the following transient heat equation by separation of variable method. aT At x = 0, BC み_Qo Atx=L, T =To IC: At t = 0, T= 1. Solve the following transient heat equation by separation of variable method. aT At x = 0, BC み_Qo Atx=L, T =To IC: At t = 0, T=
Solve the heat equation by the method of separation of variables 3π u(x,0)--2cos( x)

Solve the heat equation by the method of separation of variables 3π u(x,0)--2cos( x)
Q , Solve the heat equation in one dimension: subject to the conditions u (0,t)-u (π ,t )-0 and V (x,0) sin 3x Q , Solve the heat equation in one dimension: subject to the conditions u (0,t)-u (...

Q , Solve the heat equation in one dimension: subject to the conditions u (0,t)-u (π ,t )-0 and V (x,0) sin 3x Q , Solve the heat equation in one dimension: subject to the conditions u (0,t)-u (π ,t )-0 and V (x,0) sin 3x

2. Use the method of separation of variables to solve the boundary value problem ( au...

2. Use the method of separation of variables to solve the boundary value problem ( au = karu 0<x<L t > 0 (0,t) = 0, > 0 (1.1) -0. > 0 (u(a,0) - (x) 0<x<L. Be sure to detail exactly how f(x) enters your solution E-