Homework Answers
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
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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)...
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...
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)...
(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...
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...
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(...
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(...
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 <...
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 <.
2. Consider the initial-boundary value problem 0 0, t >0 Uz uェェ, Uz(0, t) _ u(0, t) = 0. a(z, 0...
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]...
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...
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...
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