First convert eqaution into second order differential equation,
then find value of m
after that find CF of equation in which have two constant A and B
The constant are solved by applying boundry conditions,
so finally putting the value of constants we get final solution
1. Find the weak form for the following boundary value problem: (Uxx+u = 0 u(0) =...
Solve the initial-boundary value problem for the following equation U = N Ux with U(x, 0) = sin (x) +N ,U(0, t) = 0, and U, (N, t) = 0 Q4| (5 Marks) my question please answer Solve the initial-boundary value problem for the following equation U = N Ux with U(x, 0) = sin (x) +N ,U(0, t) = 0, and U, (N, t) = 0 Q4| (5 Marks) Solve the initial-boundary value problem for the following equation Uų...
Problem 1. Find the type, transform to normal form, and solve the following PDEs. (1) uxx – 16uyy = 0 - 2uxy + (2) Uxx Uyy = 0 (3) Uxx + 5uxy + 4uyy = 0 (4) Uxx – 6uxy + 9uyy = 0 Sample Solution for Problem 1(1): Hyperbolic, wave equation. Characteristic equation y'2 – 16 = (y' + 4)(y' – 4) = 0. New variables are v = 0 = y + 4x, w = y = y...
(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) =
Problem #2115 Points) Solve the following initial-boundary-value prob- lem: u(0,t) = 1 uz(1,1) + ßu(1,1) = 1 BCs: 0 < t < oo 0 IC: u(z,0)= sin(nx)+x, 1 x by transforming it into homogeneous BCs and then solving the transformed problem Problem #2115 Points) Solve the following initial-boundary-value prob- lem: u(0,t) = 1 uz(1,1) + ßu(1,1) = 1 BCs: 0
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.
6] Find the solution u(x, y) of the following boundary value problem. u(x,0) = i, u(x, 2) = 0, a(0, y) = 0, u(3, y) = 3, 0 < x < 3 0 < y < 2. 6] Find the solution u(x, y) of the following boundary value problem. u(x,0) = i, u(x, 2) = 0, a(0, y) = 0, u(3, y) = 3, 0
30] Find th e solution of the following boundary value problem. 1<r<2, u(r, θ = 0) = 0, u(r, θ = π) =0, 1,0-0, u(r-2,0)-sin(20), 0 < θ < π. u(r Please also draw the sketch associated with this problem. You may assume that An -n2, Hn(s)sin(ns), n 1,2,3,. are the eigenpairs for the eigenvalue problem H(0) 0, H(T)0. 30] Find th e solution of the following boundary value problem. 1
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 <.
PDE questions. Please show all steps in detail. 2. Consider the initial-boundary value problem 0
1. Find the solution to the following boundary value problem on Ω (0,2) × (0,00): (102 -) u(x,t)-0 (, t) E S2 () 0, I] r E1,2 u(0, t) = u(2, t) = 2 , where t > 0 a [0,2 1. Find the solution to the following boundary value problem on Ω (0,2) × (0,00): (102 -) u(x,t)-0 (, t) E S2 () 0, I] r E1,2 u(0, t) = u(2, t) = 2 , where t > 0...