(1) (4 points) Let L 〉 0 be a given constant. Solve ut = uxx u(0,t)...
1 point) Solve the nonhomogeneous heat problem ut=uxx+4sin(2x), 0<x<π,ut=uxx+4sin(2x), 0<x<π, u(0,t)=0, u(π,t)=0u(0,t)=0, u(π,t)=0 u(x,0)=5sin(5x)u(x,0)=5sin(5x) u(x,t)=u(x,t)= Steady State Solution limt→∞u(x,t)=limt→∞u(x,t)= Please show all work. (1 point) Solve the nonhomogeneous heat problem Ut = Uxx + 4 sin(2x), 0< x < , u(0,1) = 0, tu(T, t) = 0 u(x,0) = 5 sin(52) u(a,t) Steady State Solution limt u(x, t) = Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts...
Solve the heat problem ut=uxx−cos(x), 0<x<π, ut=uxx−cos(x), 0<x<π, ux(0,t)=0, ux(π,t)=0 ux(0,t)=0, ux(π,t)=0 u(x,0)=1u(x,0)=1 u(x,t)= ?
Problem # 3 [20 Points] Solve PDE: ut = uxx - u, 0 < x < 1, 0 < t < ∞ BCs: u(0, t)=0 u(1, t)=0 0 < t < ∞ IC: u(x, 0) = sin(πx), 0 ≤ x ≤ 1 directly by separation of variables without making any preliminary trans- formation. Does your solution agree with the solution you would obtain if transformation u(x, t)= e(caret)(-t) w(x, t) were made in advance?
Solve the following problems: ut(x, t)--uxx (x, t) n(x,t), i, (x, t ) → 0, u(x,0) - e-' u, (x,t) + 2u, (x,)-u(x,t) n(x,t), u(x,0)-f(x), u.(x,0)-g(r) u,, (xs (x,t) 4 a) as|x| → t>0 b) as|x| → 0 u(x,0)-f(x), u.(r,0)-g(x) (Write the answer in the inverse Fourier Transform.) n(x, 0) = f(x) Solve the following problems: ut(x, t)--uxx (x, t) n(x,t), i, (x, t ) → 0, u(x,0) - e-' u, (x,t) + 2u, (x,)-u(x,t) n(x,t), u(x,0)-f(x), u.(x,0)-g(r) u,, (xs...
(1 point) Solve the nonhomogeneous heat problem ut = Uxx + sin(3x), 0 < x < 1, u(0,t) = 0, u1,t) = 0 u(x,0) = 2 sin(4x) u(x, t) = Steady State Solution limt-001(x, t) = ((sin(3x))/9)
3. (5 points) Find the solution u(x,t) of the equation ut = uxx, subject to the boundary conditions u(0,t) = 1, u(2,t) = 3, and the initial condition u(x,0) = 3x + 1.
(1 point) Solve the nonhomogeneous heat problem u; = Uxx + 4 sin(5x), 0 < x < t, u(0, t) = 0, u(1, t) = 0 u(x,0) = 2 sin(2x) u(x, t) = Steady State Solution limt700 u(x, t) =
If you were to solve the variant of wave equation utt=uxx+u for 0<x<6 and t>0 with u(0,t)=u(2 ,t)=0, u(x,0)=2x, ut(x,0)=0 using separation of variables, what would be the correct form of Xn (x)? Xn (x)=cosh( nπ 4 Xn (x)=sin( nπ 2 Xn (x)=sin( n2 π2 4 Xn (x)=cos nπ 2 None of these
My answers are wrong, please help (1 point) Solve the heat problem U = Uxx + sin(x) – 2 sin(2x), 0 < x < 1, u(0,t) = 0, u(,t) = 0 u(x,0) = 0 u(x,t) = sin(x)(1-e^(-1))(-sin(2x)/2)(1-e^(-4t)) Steady State Solution lim u(x,t) = 2/4(sin(2x))
PDE: Ut = Uxx, -00 < x < 0, t> 0 IC: u(x,0) = 38(x) + 28(x – 6) where is the Dirac delta function (impulse). u(x, t) =