Just need the answer and no steps.
Just need the answer and no steps. The solution of the heat equation Uxx = U7,...
6. Find the solution of the 1-dimensional heat equation on the interval 0, : Uxx, Ur (t, 0) U1(t, T) = 0, u(0, x) = 100 cos 2x 6. Find the solution of the 1-dimensional heat equation on the interval 0, : Uxx, Ur (t, 0) U1(t, T) = 0, u(0, x) = 100 cos 2x
Detail greatly appreciated thankyou Find the solution of the inhomogeneous heat equation Uxx = U/ +2,0 < x < 1,t> 0; u(0, t) = 0, u(1,t) = 0,t > 0, u(x,0) = x2 – x. Hint: Find a stationary solution first and then ..., then use the computation in Q3.
Write out the solution please Find the steady-state solution of the heat conduction equation α2uxx-ut that satisfies the given set of boundary conditions. ux(0, t)-u(0, t) = 0, u(L, t)-T v(x) = Find the steady-state solution of the heat conduction equation α2uxx-ut that satisfies the given set of boundary conditions. ux(0, t)-u(0, t) = 0, u(L, t)-T v(x) =
(a) Consider the one-dimensional heat equation for the temperature u(x, t), Ou,02u where c is the diffusivity (i) Show that a solution of the form u(x,t)-F )G(t) satisfies the heat equation, provided that 护F and where p is a real constant (ii) Show that u(x,t) has a solution of the form (,t)A cos(pr)+ Bsin(p)le -P2e2 where A and B are constants (b) Consider heat flow in a metal rod of length L = π. The ends of the rod, at...
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.
3. [4] The solution of the wave equation02, which satisfies the boundary conditions u(0,t) = u(2,t) 0, is given by a cos+b sin If u(, t) satisfies the initial conditions u(x, 0)-0 and u(x,0)3sin(Tx) - sin(3T), find the coefficients an and bn Solution: b2 = , bs =- π 97T bn-0 otherwise, and an - 0 for all n 21. 3. [4] The solution of the wave equation02, which satisfies the boundary conditions u(0,t) = u(2,t) 0, is given by...
The conductive heat transfer in a rod of length L is described by the equation au ди əraat ,0<r<L,+20 where u(x, t) is the local temperature of the rod, t is time, and a is a positive constant describing the thermal conductivity of the rod. The initial and boundary conditions are: T(r, 0) = 0, T(L, t) = 0, and T (0, 1) = 1 for > 0 (1) Find the general solution of this PDE. (11) Find the eigenvalues...
Solve the heat equation Ut = Uxx + Uyy on a square 0 <= x <= 2, 0<= y<= 2 with the following boundary and initial conditions 2. Solve the heat equation boundary conditions uvw on a square O S r s 2, 0 S vS 2 with the (note the mix of u and tu) and with initial condition 0 otherwise Present your answer as a double trigonometric sum. 2. Solve the heat equation boundary conditions uvw on a...
Find the solution by Fourier series of the heat equation with nonhomogeneous boundary conditions. Assume that the initial condition is given byf(x) uo u(0,t) = uo, u(L,t) = u1, t > 0 u(x,0) = f(x), 0 < x < L
3. Using separation of variables to solve the heat equation, u -kuxx on the interval 0x<1 with boundary conditions u(0 and ur(1, t)-0, yields the general solution, u(x, t) =A0 + Σ Ane-k,t cos(nm) (with A, = ㎡π2) 0<x<l/2 0〈x〈1,2 u(x,0)=f(x)-.., , . . .) when u(x,0) = f(x)- Determine the coefficients An (n - 0, 1,2,