Solve by d'Alembert solution PLEASE! Solve 111 = kuni 11(x, 0) 0; 11(0, 1) = 1 on the half-line 0 < x < oo Solve 111 = kuni 11(x, 0) 0; 11(0, 1) = 1 on the half-line 0

Question

Question

Solve 111 = kuni 11(x, 0) 0; 11(0, 1) = 1 on the half-line 0 < x < oo

Solve by d'Alembert solution PLEASE!

Answer 1

Answer #1

An even dote deb d t Scanned with Camscanner onstant 2 2 Sim ) o Grive ot) Et.-k (A cos (R2) +B.GBx)ご LX,卜) VIII u CS Scanned with CamScanner

Answer 2

Similar Homework Help Questions

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.
MATH2018 Quiz The PDE ar2 can be solved using D'Alembert method. That is, it has a solution of the form u(x, t) = φ(x + ct) + ψ(x-ct). where c 6 Solve the PDE with the initial conditions u(x, 0)...

MATH2018 Quiz The PDE ar2 can be solved using D'Alembert method. That is, it has a solution of the form u(x, t) = φ(x + ct) + ψ(x-ct). where c 6 Solve the PDE with the initial conditions u(x, 0) 6 sin (x), ut (x, 0) 3 er Enter the expression for u(x, t) in the box below using Maple syntax. Note: the expression should be in terms of x andt, but not c MATH2018 Quiz The PDE ar2 can...
5. (20 pts). Solve the following initial-value problem: Ut + 2uuz - 0<x<, 0 <t<oo 0...

5. (20 pts). Solve the following initial-value problem: Ut + 2uuz - 0<x<, 0 <t<oo 0 1 <1 > 1 u(t,0) = Then draw the solution for different values of time.

Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At...

Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At time t = 0, the initial condition is given by u (x,0)-0 a) Take the Fourier transform on x and show that the above PDE can be transformed into the following ODE where G() is the Fourier transform of g(x) and U(w,...
d1= 3 & d2= 2 Question 2 Find the solution 11(x, 1) for the 1-D wave equation aT = (a) 25-for -o <x < oo with initial conditions it (x,0) = A (x) , where A(x) is presented in the diagram bel...

d1= 3 & d2= 2 Question 2 Find the solution 11(x, 1) for the 1-D wave equation aT = (a) 25-for -o <x < oo with initial conditions it (x,0) = A (x) , where A(x) is presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and 1, somewhat similar to fex) on page 8s of the Notes Part 2. 2 d2+5 r-0 di+10 di+15 di+20 3...
pls solve Problem 1: Solve the initial value / Dirichlet problem on the half-line and find...

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.

5. Solve the initial boundary problem Uz(x,t) = urr(x, t), 0 < x < 2, 0 < t < oo t4(0,t) = ur(2, t) = 0, 0...

5. Solve the initial boundary problem Uz(x,t) = urr(x, t), 0 < x < 2, 0 < t < oo t4(0,t) = ur(2, t) = 0, 0 < t < 0 cos (,) 0-1(1 13 <2 Hint: Recall that the solution of a 1-d heat equation with insulated ends is given by a(x, t) c + 2 an exp | --(7 Kt cos [8 marks]
Solve equation and please state if; no solutions were lost, the solution x = 0 was...

Solve equation and please state if; no solutions were lost, the solution x = 0 was lost or the solution y=0 was lost. Thank you Solve the equation. (2x)dx + (y - 3x²y = 1)dy = 0 by multiplying by the integrating factor. An implicit solution in the form F(x,y) = C is = C, where C is an arbitrary constant, and (Type an expression using x and y as the variables.) no solutions were lost the solution x=0 was...
Problem 1: Solve the initial value / Dirichlet problem on the half-line and find the value...

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.

Please Explain 5. (4 pts) Solve the following Neumann problem on the half-line ( vt –...

Please Explain 5. (4 pts) Solve the following Neumann problem on the half-line ( vt – Vzx = 8(t – 118(x – 3), x > 0, t> 0, v(x, 0) = S(x - 2), x > 0 | vx(0,t) = 0, t > 0. The answer should be computed explicitly and must not contain the "ſ" symbol.