Solve the heat flow problem: au t> 0, ди (x, t) = 2 (x, t), 0<x< 1, ot дх2 uz(0, t) = uz(1,t) = 0, t>0, u(x,0) = 1- x, 0 < x < 1.
(1 point) Solve the heat problem U4 = Uxx, 0 < x < 1, uz (0,t) = 0, uz(t,t) = 0 u(x,0) = cos? (x) (THINK) u(x, t) =
Solve the heat flow problem: ди ди - (x, t) = 2 — (x, t), 0<x<1, t> 0, д дх2 и(0, t) = (1,1) = 0, t>0, и(x, 0) = 1 +3 cos(x) – 2 cos(3лх), 0<x<1.
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.
(1 point) Solve the heat problem with non-homogeneous boundary conditions du (x, 1) = ot (x,1), 0<x<2, t> 0 dx (0,t) = 0, (2, 1) = 2, t> 0, u(x,0) = 0<x<2. Recall that we find h(x), set u(x, t) = u(x, t)-h(x), solve a heat problem for u(x, t) and write u(x, t) = u(x, t) + h(x). Find h(x) h(x) = The solution u(x, t) can be written as u(x, t) = h(x) + u(x, t), where u(x,...
Solve using the Laplace Transform the problem with border values au x2 au at2 para 0<x<1,7 > 0 sujeto a las condiciones u(0,t) = 0, u(,0) = 0, ди u(1,t) = 0 2 sin(72) + 4 sin(372) at lt=0
FInd u(x,t) and lim u(x,t) Solve the heat problem Ut = Uzx + 5 sin(4x) - sin(2x), 0 < x <7, u(0,1) = 0, u(,t) = 0 u(x,0) = 0
2. Solve the heat problem: (Trench: Sec 12.1, 17) 9Uxx = ut, 0 < x < 4, t > 0 u(0, t) = 0, u(4,t) = 0, t> 0 u(3,0) = x2, 0 < x < 4
(1 point) Solve the nonhomogeneous heat problem Ut = uzz + sin(4x), 0 < x < , u(0,t) = 0, u(1,t) = 0 u(x,0) = 5 sin(3x) u(x, t) = Steady State Solution lim700 u(x, t) =
(1 point) Solve the heat problem uturr-Cos (x), 0 < x < T, и, (0, t) — 0, и, (т, t) — 0 и(т, 0) — 1 и(т, t) — u(x, t) = Steady State Solution lim