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Problem 5: Consider the initial value Dirichlet problem ur(t, x) - 2uzz(t, x) = e, (t,...
Problem 5: Consider the initial value Dirichlet problem ut(t, x) – 2uxx(t, x) = et, (t, x) € (0, +00)?, u(0,x) = 1, u(t,0) = e- For the unique solution u(x, t) find the following limit as a function of t: (8 points) lim u2, t). +00
Problem 5: Consider the initial value / Dirichlet problem ut(t, x) – 2uzz(t, x) = et, (t, x) € (0, +00)?, u(0, 2) = 1, u(t,0) = e- For the unique solution u(x, t) find the following limit as a function of t: (8 points) lim u(x, t). 2+
please only use substaction method or method of recflection Problem 5: Consider the initial value / Dirichlet problem ut(t, x) – 2uzz(t, x) = e, (t, x) € (0, +00), u(0,x) = 1, u(t,0) = e- For the unique solution u(x, t) find the following limit as a function of t: (8 points) lim u(x, t).
pls solve Problem 1: Solve the initial value / Dirichlet problem on the half-line and find the value u(1, 2): (8 points) uu(t, x) – uzz(t, x) = x +t, (t, x) € Rx [0, +00), u(0, 2) = cos(V), U(0,x) = e, u(t,0) = 1+t.
Problem 1: Solve the initial value / Dirichlet problem on the half-line and find the value u(1, 2): (8 points) Utt(t, 2) – Uzz(t, x) = x+t, (t, x) ER [0, +co), u(0,x) = = cos(2), ut(0, 2) = e", u(t,0) = 1+t.
The solution to the initial value problem below takes on different forms for different ranges of the parameter ζ, which is called the dimensionless damping coefficient. In each case, write the solution in the suggested form. u'' + 6 ζ u' +9u = 0 u(0) = 0 u'(0) = 1 If ζ > 1 , uζ(t) = e( Incorrect: Your answer is incorrect. ) sinh( Incorrect: Your answer is incorrect. ) Incorrect: Your answer is incorrect. Compute the limit as...
Problem 1: Solve the initial value Dirichlet problem on the half-line and find the value u(1, 2): (8 points) tut(t, z) - trọt, c) = c+t, (t, x) R x [0, +x), u(0, 2) = cos(V), 4(0,2)=e", u(t,0) = 1+ t.
Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x,t) represents the temperature. 9uxx = upi 0<x< 6; t> 0; B.C.: uz(0,t) = 0; ux, t) = 0; t> 0; 1.C.:u(x,0) = 12 + 5cos 6 x) – 4cos(26x); 0<x<6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or mixed...
Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0<x< 6; t> 0; B.C.: ux(0,t) = 0; uz(6,t) = 0; t> 0; I. C.: u(x,0) = 12 + 5cos (x) – 4cos(27x); 0<x< 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or...
Please help Find the solution to the initial value problem: x(0)-0x(O)--1 x(t) write x(t) as a product of a sine and a cosine, one with the beat (slow) frequency (μ-2)/2 , and the other with the carrier (fast) frequency (μ+ 2)/2 x(t) The solution x(t) is really a function of two variables t and μ . Compute the limit of x(t씨 as μ approaches 2 (your answer should be a function of t. lim x(t,H) Define y(t)-lim x(t,u) What differential...