2. (P5, page 105, 10pts) Solve the following initial-boundary value problem: utt = 90 , tu(0,1)...
1. (P1, page 68, 10pts) Solve the following initial-boundary value problem: ut = kuzi+t, (2,0) = 2(L-1), (0, 1) = 0, u(Lit) = 0, for 0<x<L, t > 0, for 0 <r<L, for t>0, for t>
22: Solve the follwing boundary value problem Ugex - 2 = Utt: 0 < x < 1, t> 0, u(0, 1) = 0, u(1,t) = 0, 0 < x < 1, u(x,0) = x2 - x, ut(x,0) = 1, t > 0. Solve the follwing boundary value problem Uxx + e-3t = ut, 0 < x < t, t > 0, ux(0,t) = 0, unt,t) = 0, t>0, u(x,0) = 1, 0 < x <.
Solve the initial-boundary value problem. Theorem 11.3.5 (b) will simplify the computa- tion of the coefficients in the Fourier sine series. 64uz 0<x<3, t>0, u(0,t) = 0, u(3, t) = 0, t > 0, u(x,0) = (22 – 9), ut(2,0) = 0, 0<x<3. Utt
5. Consider the following IBVP (initial boundary value problem utt - Curr = 0, 0<x<1, t>0, with boundary conditions u(0,t) = u(1, t) = 0, > 0 and initial conditions (7,0) = x(1 – 2), 14(2,0) = 0, 0<x< 1. Use separation of variables method to find an infinite series solution of this problem. Do a complete calculation for this problem.
In Exercises 1-15 solve the initial-boundary value problem. In some of these exercises, Theorem 11.3.5(b) or Exercise 11.3.35 will simplify the computation of the coefficients in the Fourier sine series. 6. Utt = 64uxx, (<r <3, t> 0, u(0,0) = 0, (3, 1) = 0, t>0, u(2,0) = (:2 – 9), ur(2,0) = 0, 0<x<3
I need help with this PDE problem, part A and D 4.2.3. Write down the solutions to the following initial-boundary value problems for the wave equation in the form of a Fourier series: a) utt = uzz , u(t, 0) = u(t, π) = 0, u(0,x) = 1, ut(0,z) = 0; (b) utt = 2uxx, a(t, 0) = u(t, π) = 0, a(0,x) = 0, ut(0,x) = 1; c) utt = 3uzz , ti(t, 0)=u(t, π)=0, u(0,x) = sin3 x,...
2. Solve the initial-boundary value problem One = 48m2 for 0 < x < 8, t > 0, u(0, t) = u(8,t) = 0 for t > 0, u(2,0) = 2e-4x for 0 < x < 8. (60 pts.)
6.[10] Find the solution to the vibrating string problem governed by the given initial-boundary value problem: 9uxx = Utt 0<x< 1, t> 0 u(0,t) = 0) = u(tt,t), t> 0 u(x,0) = sin 4x + 7 sin 5x, 0<x< 1 uz (3,0) = { X, 0 < x < 1/2 r/2 < x <
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.
In Exercises 1-15 solve the initial-boundary value problem. In some of these exercises, Theorem 11.3.5(b) or Exercise 11.3.35 will simplify the computation of the coefficients in the Fourier sine series. 8. Cutt 64uzz, 0<<<3, t> 0, u(0, 1) = 0, ta(3, 1) = 0, t> 0, u(x,0)=0, ut(3,0) = (x2 – 9), 0 < x <3