Homework Answers
Add Answer to:
7.17 (a) Solve the equation u, 2u, in the domain 0< x<T, t>0 under the initial...
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
Find the solution to the heat equation on the infinite domain ∂u∂t=k∂2u∂x2,−∞<x<∞,t>0,u(x,0)={x,0,|x|<1|x|>1.∂u∂t=k∂2u∂x2,−∞<x<∞,t>0,u(x,0)={x,|x|<10,|x|>1. in terms of the...
Find the solution to the heat equation on the infinite
domain
∂u∂t=k∂2u∂x2,−∞<x<∞,t>0,u(x,0)={x,0,|x|<1|x|>1.∂u∂t=k∂2u∂x2,−∞<x<∞,t>0,u(x,0)={x,|x|<10,|x|>1.
in terms of the error function.
Q1 (10 points) Find the solution to the heat equation on the infinite domain azu ди at k -00<x<0, t>0, ar2 u(x,0) (X, 1x < 1 10, [] > 1. in terms of the error function. + Drag and drop your files or click to browse...
(1 point) Solve the heat problem with non-homogeneous boundary conditions ∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0 u(0,t)=0, u(3,t)=2, t>0,
(1 point) Solve the heat problem with non-homogeneous boundary
conditions
∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0
u(0,t)=0, u(3,t)=2, t>0,u(0,t)=0, u(3,t)=2, t>0,
u(x,0)=23x, 0<x<3.u(x,0)=23x, 0<x<3.
Recall that we find h(x)h(x), set
v(x,t)=u(x,t)−h(x)v(x,t)=u(x,t)−h(x), solve a heat problem for
v(x,t)v(x,t) and write u(x,t)=v(x,t)+h(x)u(x,t)=v(x,t)+h(x).
Find h(x)h(x)
h(x)=h(x)=
The solution u(x,t)u(x,t) can be written as
u(x,t)=h(x)+v(x,t),u(x,t)=h(x)+v(x,t),
where
v(x,t)=∑n=1∞aneλntϕn(x)v(x,t)=∑n=1∞aneλntϕn(x)
v(x,t)=∑n=1∞v(x,t)=∑n=1∞
Finally, find
limt→∞u(x,t)=limt→∞u(x,t)=
Please show all work.
(1 point) Solve the heat problem with non-homogeneous boundary conditions au ди (x, t) at (2, t), 0<x<3, t> 0 ar2 u(0,t) = 0, u(3, t) = 2, t>0, u(t,0)...
Solve the wave equation a2 ∂2u ∂x2 = ∂2u ∂t2 , 0 < x < L,...
Solve the wave equation
a2
∂2u
∂x2
=
∂2u
∂t2
, 0 < x < L, t > 0
(see (1) in Section 12.4) subject to the given conditions.
u(0, t) = 0, u(L, t) = 0
u(x, 0) =
4hx
L
,
0
<
x
<
L
2
4h
1 −
x
L
,
L
2
≤
x
<
L
,
∂u
∂t
t = 0
= 0
We were unable to transcribe this imageWe were unable to transcribe...
Solve the equation yu- xui = u, t > 0,x >0 with the initial conditions u(x,...
Solve the equation yu- xui = u, t > 0,x >0 with the initial conditions u(x, 0) =1 + x2 using the method of characteristics. Find the u(x, y). Substitute your found solution u(x, y) in the equation and verify that it satisfies the equation. solution explicitly in the form u =
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 equation for u(x, t) if it satisfies the equation: with boundary and initial conditions...
Solve the equation for u(x, t) if it satisfies the equation: with boundary and initial conditions given by where δ(x) and δ(t) are Dirac delta functions. 2. du-Ka_ = δ(x-a)s(t) for 0 < x < oo; t > 0 at ах? du ах (0, t) = 0;u(co, t) =0;(mt) = 0; u(x, 0)=0 ox
Solve the equation for u(x, t) if it satisfies the equation: with boundary and initial conditions given by where δ(x) and δ(t) are Dirac delta functions....
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
25 points) Find the solution of the Laplace equation ur the domain 0-x-π and 0-y-T. The...
25 points) Find the solution of the Laplace equation ur the domain 0-x-π and 0-y-T. The boundary condition at the left boundary is given by u(0, y)-sin(y/2). The boundary conditions at al other boundaries are zero. Express the solution as an infinite series = 0, over
Consider the second order partial differential equation du/dt= d^2u/dx^2 +2du/dx+u over the domain x in [0,l) and t>=...
Consider the second order partial differential equation du/dt=
d^2u/dx^2 +2du/dx+u over the domain x in [0,l) and t>=0. It is
given that u(0,t)=u(l,t)=0. Use the method of separation of
variables to prove that the general solution with the given
boundary condition is u(x,t)= infinity series n=1
bnsin(npix/l)exp(-x-((npi/l)^2)t) where bn is
a constant for every n N
Hint u(x,t)=X(x)T(t)
tnsit te Seind ond partial difertinl cuatan +2n St the dowain e To,e) an Use metod o Separet ion Vaiades to rore...
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
Find the solution to the heat equation on the infinite
domain
∂u∂t=k∂2u∂x2,−∞<x<∞,t>0,u(x,0)={x,0,|x|<1|x|>1.∂u∂t=k∂2u∂x2,−∞<x<∞,t>0,u(x,0)={x,|x|<10,|x|>1.
in terms of the error function.
Q1 (10 points) Find the solution to the heat equation on the infinite domain azu ди at k -00<x<0, t>0, ar2 u(x,0) (X, 1x < 1 10, [] > 1. in terms of the error function. + Drag and drop your files or click to browse...
(1 point) Solve the heat problem with non-homogeneous boundary
conditions
∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0
u(0,t)=0, u(3,t)=2, t>0,u(0,t)=0, u(3,t)=2, t>0,
u(x,0)=23x, 0<x<3.u(x,0)=23x, 0<x<3.
Recall that we find h(x)h(x), set
v(x,t)=u(x,t)−h(x)v(x,t)=u(x,t)−h(x), solve a heat problem for
v(x,t)v(x,t) and write u(x,t)=v(x,t)+h(x)u(x,t)=v(x,t)+h(x).
Find h(x)h(x)
h(x)=h(x)=
The solution u(x,t)u(x,t) can be written as
u(x,t)=h(x)+v(x,t),u(x,t)=h(x)+v(x,t),
where
v(x,t)=∑n=1∞aneλntϕn(x)v(x,t)=∑n=1∞aneλntϕn(x)
v(x,t)=∑n=1∞v(x,t)=∑n=1∞
Finally, find
limt→∞u(x,t)=limt→∞u(x,t)=
Please show all work.
(1 point) Solve the heat problem with non-homogeneous boundary conditions au ди (x, t) at (2, t), 0<x<3, t> 0 ar2 u(0,t) = 0, u(3, t) = 2, t>0, u(t,0)...
Solve the wave equation
a2
∂2u
∂x2
=
∂2u
∂t2
, 0 < x < L, t > 0
(see (1) in Section 12.4) subject to the given conditions.
u(0, t) = 0, u(L, t) = 0
u(x, 0) =
4hx
L
,
0
<
x
<
L
2
4h
1 −
x
L
,
L
2
≤
x
<
L
,
∂u
∂t
t = 0
= 0
We were unable to transcribe this imageWe were unable to transcribe...
Solve the equation yu- xui = u, t > 0,x >0 with the initial conditions u(x, 0) =1 + x2 using the method of characteristics. Find the u(x, y). Substitute your found solution u(x, y) in the equation and verify that it satisfies the equation. solution explicitly in the form u =
Solve the equation for u(x, t) if it satisfies the equation: with boundary and initial conditions given by where δ(x) and δ(t) are Dirac delta functions. 2. du-Ka_ = δ(x-a)s(t) for 0 < x < oo; t > 0 at ах? du ах (0, t) = 0;u(co, t) =0;(mt) = 0; u(x, 0)=0 ox
Solve the equation for u(x, t) if it satisfies the equation: with boundary and initial conditions given by where δ(x) and δ(t) are Dirac delta functions....
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
25 points) Find the solution of the Laplace equation ur the domain 0-x-π and 0-y-T. The boundary condition at the left boundary is given by u(0, y)-sin(y/2). The boundary conditions at al other boundaries are zero. Express the solution as an infinite series = 0, over
Consider the second order partial differential equation du/dt=
d^2u/dx^2 +2du/dx+u over the domain x in [0,l) and t>=0. It is
given that u(0,t)=u(l,t)=0. Use the method of separation of
variables to prove that the general solution with the given
boundary condition is u(x,t)= infinity series n=1
bnsin(npix/l)exp(-x-((npi/l)^2)t) where bn is
a constant for every n N
Hint u(x,t)=X(x)T(t)
tnsit te Seind ond partial difertinl cuatan +2n St the dowain e To,e) an Use metod o Separet ion Vaiades to rore...
Most questions answered within 3 hours.
-
A regression equation that describes the relationship between
the amount of the bill ($) at a...
asked 2 minutes ago -
284 mL of a 0.52 M potassium hydroxide solution is added to 467
mL of a...
asked 30 minutes ago -
exercise on VSEPR and molecular structrue.
octahedral
SeCl62-
TeCl62-
ClF62-
distorted
SeF62–
IF6–
asked 31 minutes ago -
Little’s Law: Val d’Costa is a world famous ski village in the
French Alps. Because of...
asked 1 hour ago -
Find the absolute error D for the calculation if A + B/C=D A=
9.4 +/- 0.4...
asked 1 hour ago -
New Air Heating and Cooling, manufactures furnaces and central
air units. The company pride itself on...
asked 1 hour ago -
A coach uses a new technique to train gymnasts. Seven
gymnasts were randomly selected and their...
asked 3 hours ago -
While rotating the tires on your car you notice a rock [mass =
0.1 Kg] stuck...
asked 5 hours ago -
Using MARS simulator, write MIPS programs according to
the following scenarios: Receive a positive integer number...
asked 7 hours ago -
An object in front of a concave mirror has a real image that is
11.5 cm...
asked 7 hours ago -
Consider the reaction, C3 H8 + O2 --> CO2 + H2O. How many
moles of O2...
asked 9 hours ago -
You and your opponent both roll a fair die. If you both roll the
same number,...
asked 9 hours ago