please do all of the sub questions in #6. Thank you so
much!
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please do all of the sub questions in #6. Thank you so
much!
6. Find and...
please do not do question 1 but add "Assume...." conditions to #1, thank you, upvote for...
please do not do question 1 but add "Assume...." conditions to #1,
thank you, upvote for sure
Consider the heat equation on "half-line" 0 <<< with prescribed zero temperature at x = 0 U = kuzx (0,t) = 0, ,0) = f(x) [the initial temperature). Find solution of this boundary value problem in the form u(x, t) = G(x – y, t) – 6(x + y,0)) f(y)dy, where G(x, t) = ome. Hint: Extend f(x) as an odd function f(x)...
QUESTION 2 Consmder the problem ди 2k, 0<r< 1, t>O оt and the boundary conditions u(0,t)=...
QUESTION 2 Consmder the problem ди 2k, 0<r< 1, t>O оt and the boundary conditions u(0,t)= 1, u (1,t) = 3, t > 0 (a) Find the equiltbrium solutiou ug (r) (b) Find the solution u (z.t) of the PDE and the boundary condition which also satisfies the mitial condition (,0)-1+++sin (3wx), 0<o< 1 [25]
(1 point) Solve the heat problem with non-homogeneous boundary conditions du (x, 1) = ot (x,1),...
(1 point) Solve the heat problem with non-homogeneous boundary conditions du (x, 1) = ot (x,1), 0<x<2, t> 0 dx (0,t) = 0, (2, 1) = 2, t> 0, u(x,0) = 0<x<2. Recall that we find h(x), set u(x, t) = u(x, t)-h(x), solve a heat problem for u(x, t) and write u(x, t) = u(x, t) + h(x). Find h(x) h(x) = The solution u(x, t) can be written as u(x, t) = h(x) + u(x, t), where u(x,...
The conductive heat transfer in a rod of length L is described by the equation au...
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...
Thank you. 5. Find the solution u(x, y) of Laplace's equation in the rectangle 0<<a, 0<y<b...
Thank you.
5. Find the solution u(x, y) of Laplace's equation in the rectangle 0<<a, 0<y<b that satisfies the boundary conditions u(0, y = 0, u(a, y) = 0,uy 3,0) = 0, 2,b) = g(1), where J2 0<x<a/2 g(x) = - 0<a/2 <<a
Find the steady-state solution of the heat conduction equation α2uxx-ut that satisfies the given ...
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) =
Please help me with this questions, 1a) & 1b). Show all steps, thank you! ду 1....
Please help me with this questions, 1a) & 1b).
Show all steps, thank you!
ду 1. Find the general solution, u(x,y), of the following PDEs by separation of variables: ди ди (а) 0. ду Ә?и (b) = 0. дудх ди ди (c) tan(x) +y = 0. д ду ие
5. Given the initial-boundary value problem as below: ди ди at +u=k 0<x<1, 1>0, Ox?? Ou...
5. Given the initial-boundary value problem as below: ди ди at +u=k 0<x<1, 1>0, Ox?? Ou -(0,1) Ox Ou (1,t)=0, @x t>0, u(x,0) = x(1 - x) 0<x<1. where k is a non-zero positive constant. (i) By separation of variables, let the solution be in the form u(x,t) = X(x)T(t), show that one can obtain two differential equations for X(x) and T(t) as below: X"-cX = 0 and I' + (1 - ck)T = 0) where c is a constant....
=T 20 marks) Consider the following PDE with boundary and initial conditions: U = Upx +...
=T 20 marks) Consider the following PDE with boundary and initial conditions: U = Upx + ur, for 0<x< 1 and to with u(0,t) = 1, u(1,t) = 0, u(1,0) = (a) Find the steady state solution, us(1), for the PDE. (b) Let Uſz,t) = u(?, t) – us(T). Derive a PDE plus boundary and initial conditions for U(2,t). Show your working. (c) Use separation of variables to solve the resulting problem for U. You may leave the inner products...
i need help with all parts. i will rate. thank you very much. Suppose u=f x+y...
i need help with all parts. i will rate.
thank you very much.
Suppose u=f x+y ху is a differentiable function. Which equation must be true? ди ди дхду = 0 од? д?u дх2 ду? + = 0 х2. ди ди - у. дх ду = 0 ди y- дх ди Х- ду = 0 O None of the above Suppose the position vector is given by F(t) = = <t, t², 2) Then at time t = 1, the...
please do not do question 1 but add "Assume...." conditions to #1,
thank you, upvote for sure
Consider the heat equation on "half-line" 0 <<< with prescribed zero temperature at x = 0 U = kuzx (0,t) = 0, ,0) = f(x) [the initial temperature). Find solution of this boundary value problem in the form u(x, t) = G(x – y, t) – 6(x + y,0)) f(y)dy, where G(x, t) = ome. Hint: Extend f(x) as an odd function f(x)...
QUESTION 2 Consmder the problem ди 2k, 0<r< 1, t>O оt and the boundary conditions u(0,t)= 1, u (1,t) = 3, t > 0 (a) Find the equiltbrium solutiou ug (r) (b) Find the solution u (z.t) of the PDE and the boundary condition which also satisfies the mitial condition (,0)-1+++sin (3wx), 0<o< 1 [25]
(1 point) Solve the heat problem with non-homogeneous boundary conditions du (x, 1) = ot (x,1), 0<x<2, t> 0 dx (0,t) = 0, (2, 1) = 2, t> 0, u(x,0) = 0<x<2. Recall that we find h(x), set u(x, t) = u(x, t)-h(x), solve a heat problem for u(x, t) and write u(x, t) = u(x, t) + h(x). Find h(x) h(x) = The solution u(x, t) can be written as u(x, t) = h(x) + u(x, t), where u(x,...
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...
Thank you.
5. Find the solution u(x, y) of Laplace's equation in the rectangle 0<<a, 0<y<b that satisfies the boundary conditions u(0, y = 0, u(a, y) = 0,uy 3,0) = 0, 2,b) = g(1), where J2 0<x<a/2 g(x) = - 0<a/2 <<a
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) =
Please help me with this questions, 1a) & 1b).
Show all steps, thank you!
ду 1. Find the general solution, u(x,y), of the following PDEs by separation of variables: ди ди (а) 0. ду Ә?и (b) = 0. дудх ди ди (c) tan(x) +y = 0. д ду ие
5. Given the initial-boundary value problem as below: ди ди at +u=k 0<x<1, 1>0, Ox?? Ou -(0,1) Ox Ou (1,t)=0, @x t>0, u(x,0) = x(1 - x) 0<x<1. where k is a non-zero positive constant. (i) By separation of variables, let the solution be in the form u(x,t) = X(x)T(t), show that one can obtain two differential equations for X(x) and T(t) as below: X"-cX = 0 and I' + (1 - ck)T = 0) where c is a constant....
=T 20 marks) Consider the following PDE with boundary and initial conditions: U = Upx + ur, for 0<x< 1 and to with u(0,t) = 1, u(1,t) = 0, u(1,0) = (a) Find the steady state solution, us(1), for the PDE. (b) Let Uſz,t) = u(?, t) – us(T). Derive a PDE plus boundary and initial conditions for U(2,t). Show your working. (c) Use separation of variables to solve the resulting problem for U. You may leave the inner products...
i need help with all parts. i will rate.
thank you very much.
Suppose u=f x+y ху is a differentiable function. Which equation must be true? ди ди дхду = 0 од? д?u дх2 ду? + = 0 х2. ди ди - у. дх ду = 0 ди y- дх ди Х- ду = 0 O None of the above Suppose the position vector is given by F(t) = = <t, t², 2) Then at time t = 1, the...
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