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Solve the following homogeneous wave equation: un (2. t) = 4uxx(x, t), u(0.t) = u(t) =...
1. Consider the following inhomogeneous wave equation on (0,7) : utt - 4uxx = (1 -...
1. Consider the following inhomogeneous wave equation on (0,7) : utt - 4uxx = (1 - x) cost Uz(0,t) = cost-1, uz(7,t) = cost u(3,0) = 2(7,0) = cos 3x (a) Convert the PDE to an equation with homogeneous boundary conditions by making an appropriate substitution u(x, t) = u(x, t) - p(x, t), implying u(,t) = v(x, t) + p(2,t) for an appropriate function p(x, t). (b) Finish solving the PDE using the Method of Eigenfunction expansion.
9. Solve the wave equation subject to the boundary and initial conditions u(0,t) = 0, u(x,0)...
9. Solve the wave equation subject to the boundary and initial conditions u(0,t) = 0, u(x,0) = 0, U(TT, t) = 0, t> 0 $ (3,0) = sin(x), 0<x<a
3. Solve the wave equation subject to the conditions u(0,t)=0, u(z,t) = 0 at 2 2...
3. Solve the wave equation subject to the conditions u(0,t)=0, u(z,t) = 0 at 2 2 u(x, 0) = 4 =0 at 2 =1
3. Solve the wave equation subject to the conditions u(0,t)=0, u(z,t) = 0 at 2 2 u(x, 0) = 4 =0 at 2 =1
Problem 2. Solve the following wave equation. Utt = Ucx + x for t > 0...
Problem 2. Solve the following wave equation. Utt = Ucx + x for t > 0 and 0 < x < 1 Boundary Conditions: u(0,t) = 0 AND u(1,t) = 1 Inital Condition: u(x,0) = $(x) AND u1(x,0) = 0
(2) Solve the following BVP for the Wave Equation using the Fourier Serics solution formulac (42- u(r, t)= 0 u(0, t) 0...
(2) Solve the following BVP for the Wave Equation using the Fourier Serics solution formulac (42- u(r, t)= 0 u(0, t) 0 u(5, t) 0 u(r, 0) sin(T) 12sin(T) ut(r, 0)0 (r, t) E (0,5) x (0, oo) t > 0 t > 0
(2) Solve the following BVP for the Wave Equation using the Fourier Serics solution formulac (42- u(r, t)= 0 u(0, t) 0 u(5, t) 0 u(r, 0) sin(T) 12sin(T) ut(r, 0)0 (r, t) E (0,5) x...
For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)...
For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition:
For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition:
Solve the BVP for the wave equation (∂^2u)/(∂t^2)(x,t)=(∂^2u)/(∂x^2)(x,t), 0<x<5pi u(0,t)=0, u(5π,t)=0, t>0, u(x,0)=sin(2x), ut(x,0)=4sin(5x), 0<x<5pi. u(x,t)=
Solve the BVP for the wave equation (∂^2u)/(∂t^2)(x,t)=(∂^2u)/(∂x^2)(x,t), 0<x<5pi u(0,t)=0, u(5π,t)=0, t>0, u(x,0)=sin(2x), ut(x,0)=4sin(5x), 0<x<5pi. u(x,t)=
Solve the IBVP wave equation. d^2/dt^2=16d^2/dx^2 0<x<pi u(x,0)=sinx du(x,0)/dt=0 u(0,t)=u(pi,t) =0 t>0
Solve the IBVP wave equation. d^2/dt^2=16d^2/dx^2 0<x<pi u(x,0)=sinx du(x,0)/dt=0 u(0,t)=u(pi,t) =0 t>0
Solve the wave equation on the domain 0 < x < , t > 0 ?...
Solve the wave equation on the domain 0 < x < , t > 0 ? uxx Utt = with the boundary condition u (0, t) = 0 and the initial conditions u (x,0) = x2 u (x,0) = x
3. Using the linearity of the wave equation, solve the wave equation problem 82u 2 82u a(0, t) = 0 u(L,t)0 u(z,0) = sin( ) (z, 0) = sin( F) 3. Using the linearity of the wave equation, solve the...
3. Using the linearity of the wave equation, solve the wave equation problem 82u 2 82u a(0, t) = 0 u(L,t)0 u(z,0) = sin( ) (z, 0) = sin( F)
3. Using the linearity of the wave equation, solve the wave equation problem 82u 2 82u a(0, t) = 0 u(L,t)0 u(z,0) = sin( ) (z, 0) = sin( F)
1. Consider the following inhomogeneous wave equation on (0,7) : utt - 4uxx = (1 - x) cost Uz(0,t) = cost-1, uz(7,t) = cost u(3,0) = 2(7,0) = cos 3x (a) Convert the PDE to an equation with homogeneous boundary conditions by making an appropriate substitution u(x, t) = u(x, t) - p(x, t), implying u(,t) = v(x, t) + p(2,t) for an appropriate function p(x, t). (b) Finish solving the PDE using the Method of Eigenfunction expansion.
9. Solve the wave equation subject to the boundary and initial conditions u(0,t) = 0, u(x,0) = 0, U(TT, t) = 0, t> 0 $ (3,0) = sin(x), 0<x<a
3. Solve the wave equation subject to the conditions u(0,t)=0, u(z,t) = 0 at 2 2 u(x, 0) = 4 =0 at 2 =1
3. Solve the wave equation subject to the conditions u(0,t)=0, u(z,t) = 0 at 2 2 u(x, 0) = 4 =0 at 2 =1
Problem 2. Solve the following wave equation. Utt = Ucx + x for t > 0 and 0 < x < 1 Boundary Conditions: u(0,t) = 0 AND u(1,t) = 1 Inital Condition: u(x,0) = $(x) AND u1(x,0) = 0
(2) Solve the following BVP for the Wave Equation using the Fourier Serics solution formulac (42- u(r, t)= 0 u(0, t) 0 u(5, t) 0 u(r, 0) sin(T) 12sin(T) ut(r, 0)0 (r, t) E (0,5) x (0, oo) t > 0 t > 0
(2) Solve the following BVP for the Wave Equation using the Fourier Serics solution formulac (42- u(r, t)= 0 u(0, t) 0 u(5, t) 0 u(r, 0) sin(T) 12sin(T) ut(r, 0)0 (r, t) E (0,5) x...
For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition:
For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition:
Solve the wave equation on the domain 0 < x < , t > 0 ? uxx Utt = with the boundary condition u (0, t) = 0 and the initial conditions u (x,0) = x2 u (x,0) = x
3. Using the linearity of the wave equation, solve the wave equation problem 82u 2 82u a(0, t) = 0 u(L,t)0 u(z,0) = sin( ) (z, 0) = sin( F)
3. Using the linearity of the wave equation, solve the wave equation problem 82u 2 82u a(0, t) = 0 u(L,t)0 u(z,0) = sin( ) (z, 0) = sin( F)
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