PART III 3. Use the method of of t Conduction probleparation of Variables to find the solution of...
PART III 3. Use the method of of t Conduction probleparation of Variables to find the solution of a givern A. ut (x, t)-(0.16) uxx (x, t) u(0, t) = u(8, t) = 0 , t > O u(x, 0)= |x-41, o<x<b t> 0,0<x<8 or
part A PART IV. 4. Use the Vibration problem. method of Separation of Variables to find the solution of a String A. Ue (x, t)-0.16us (x, ) 0,0x<8 u(0, t)u(8, t)-0,t0 u(x, 0) = 0 , 0
Find the solution of the heat conduction problem and provide a detailed graph showing the initial, intermediate and final temperature distribution in the bar. 3. ut uxx ux(0, t) 0 ux(1,t) 0 u(x, 0) 1-x Find the solution of the heat conduction problem and provide a detailed graph showing the initial, intermediate and final temperature distribution in the bar. 4. ut = 2uxx u(0,t) 0 u(10,t) 10 u(x, 0) = 10 Find the solution of the heat conduction problem and...
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.
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) =
4. Use the method of eigenfunction expansion to find the solution of the IBVP ut (x, t) u (0,t) u (x, 0) ura' (a, t) + 2t sin (2na:) , 0 < x < 1, 0, u(1,t)=0, t > 0, sin(2π.r)-5 sin (4π.r) , 0 < x < 1. t > 0, = = = 4. Use the method of eigenfunction expansion to find the solution of the IBVP ut (x, t) u (0,t) u (x, 0) ura' (a, t)...
Use the method of separation of variables to find all possible product solutions of x2 Uxx + Uyy + 3 x Ux + 2uy +u = 0.
7. Find the solution of the heat conduction problem 100uzz = ut, 0 < x < 1, t > 0; u(0,t) 0, u1,t 0, t>0; In Problem 10, consider the conduction of heat in a rod 40 cm in length whose ends are maintained at 0°C for all t0. Find an expression for the temperature u(,t) if the initial temperature distribution in the rod is the given function. Suppose that a
Problem 2. Find the type, transform to normal form, and find the solution u(x,t) of the ID wave equation, Utt = Uxx, with the initial conditions u(x,0) = 2sin 2x and ut(x,0) = 0 and the boundary conditions u(0,t) = u(nt,t) = 0.
3. Use separation of variables to compute the first five terms of the series solution of the IBVP: urr (r,0) + r-rur (r, θ u (1,0, t) 0, u (r, θ, t) , ur(r, θ, t) bounded as r-+0+,-π < θ < π, t > 0, u (r,0,0) = r sin θ, ut (r.0, 0) = 0, o < r < 1, -π < θ < π. Hint: Follow the example from Lecture 19 and use the fact that with...