Find the solution to the heat equation on 0 < x < l,
with u(0, t)...
Find the solution to the heat equation on 0 < x < l,
with u(0, t) = 0, ux(l, t) = 0, and u(x, 0) =
phi(x).
This is sometimes called a "mixed" boundary condition.
Heat equation: Arbitrary temperatures at ends. If the ends x =
0 and x = L of the bar in the text are kept at constant
temperatures U1 and U2, respectively. The initial temp distribution
is given by u(x, 0) = f (x).
(a) What is the temperature u1(x) in the bar after a long time
(theoretically, as t → ∞)? First guess, then calculate.
(b) What is the temperature at any t. Use the heat equation
given by ut...
Consider the equation: ?̇ +2? = ?(?) with initial condition x(0)
= 2
(a) If u(t) = 0, find the solution ?(?). What is ?(?) as t ->
∞?
(b) If u(t) = 4+t, find the solution ?(?). What is ?(?) as t
-> ∞?
(c) If u(t) = ?3?, find the solution ?(?). What is
?(?) as t -> ∞?
(d) If u(t) = δ(t), find the solution ?(?). What is ?(?) as t
-> ∞?
Find the unique solution u of the parabolic boundary value
problem
Ut −Uxx =e^(−t)*sin(3x), 0<x<π, t>0,
U(0,t) = U(π,t) = 0, t > 0,
U(x, 0) = e^(π), 0 ≤ x ≤ π.
utility function u(x,y;t )= (x-t)ay1-a
x>=t, t>0, 0<a<1
u(x,y;t )=0 when x<t
does income consumption curve is
y=[(1-a)(x-t)px]/apy ?(my result, i used
lagrange, not sure about it)
how to draw the income consumption curve?