Question

Heat Problem Solve the following IBVPs for the heat equation: $frac{partial u}{partial t} = 2 frac{partial^2 u}{partial x^2}$, 0 < x < ?, t > 0 1. u(t, 0) = 0, t ? 0 u(t, ?) = 0, t ? 0 u(0, x) = sin 3x - sin 5x, 0 ? x ? ? $frac{partial u}{partial t} = frac{partial^2 u}{partial x^2}$, 0 < x < ?, t > 0 $frac{partial u}{partial x}$(t, 0) = 0, t ? 0 2. $frac{partial u}{partial x}$(t, ?) = 0, t ? 0 u(0, x) = 1 - cos 10x, 0 ? x ? ? $frac{partial u}{partial t} = 3 frac{partial^2 u}{partial x^2}$, 0 < x < ?, t > 0 $frac{partial u}{partial x}$(t, 0) = 0, t ? 0 3. $frac{partial u}{partial x}$(t, ?) = 0, t ? 0 u(0, x) = x, 0 ? x ? ? $frac{partial u}{partial t} = 2 frac{partial^2 u}{partial x^2}$, 0 < x < ?, t > 0 4. u(t, 0) = 0, t ? 0 u(t, ?) = 0, t ? 0 u(0, x) = 0, 0 ? x ? ? $frac{partial u}{partial t} = 4 frac{partial^2 u}{partial x^2}$, 0 < x < ?, t > 0 $frac{partial u}{partial x}$(t, 0) = 0, t ? 0 5. u(t, ?) = 0, t ? 0 u(0, x) = -?, 0 ? x ? ? 1

          Heat Problem
Solve the following IBVPs for the heat equation:
$frac{partial u}{partial t} = 2 frac{partial^2 u}{partial x^2}$,  0 < x < ?, t > 0
1.
u(t, 0) = 0, t ? 0
u(t, ?) = 0, t ? 0
u(0, x) = sin 3x - sin 5x, 0 ? x ? ?
$frac{partial u}{partial t} = frac{partial^2 u}{partial x^2}$,  0 < x < ?, t > 0
$frac{partial u}{partial x}$(t, 0) = 0, t ? 0
2.
$frac{partial u}{partial x}$(t, ?) = 0, t ? 0
u(0, x) = 1 - cos 10x, 0 ? x ? ?
$frac{partial u}{partial t} = 3 frac{partial^2 u}{partial x^2}$, 0 < x < ?, t > 0
$frac{partial u}{partial x}$(t, 0) = 0, t ? 0
3.
$frac{partial u}{partial x}$(t, ?) = 0, t ? 0
u(0, x) = x, 0 ? x ? ?
$frac{partial u}{partial t} = 2 frac{partial^2 u}{partial x^2}$, 0 < x < ?, t > 0
4.
u(t, 0) = 0, t ? 0
u(t, ?) = 0, t ? 0
u(0, x) = 0, 0 ? x ? ?
$frac{partial u}{partial t} = 4 frac{partial^2 u}{partial x^2}$, 0 < x < ?, t > 0
$frac{partial u}{partial x}$(t, 0) = 0, t ? 0
5.
u(t, ?) = 0, t ? 0
u(0, x) = -?, 0 ? x ? ?
1

$Heat Problem Solve the following IBVPs for the heat equation: fracpartial upartial t = 2 fracpartial^2 upartial x^2, 0 < x < ?, t > 0 1. u(t, 0) = 0, t ? 0 u(t, ?) = 0, t ? 0 u(0, x) = sin 3x - sin 5x, 0 ? x ? ? fracpartial upartial t = fracpartial^2 upartial x^2, 0 < x < ?, t > 0 fracpartial upartial x(t, 0) = 0, t ? 0 2. fracpartial upartial x(t, ?) = 0, t ? 0 u(0, x) = 1 - cos 10x, 0 ? x ? ? fracpartial upartial t = 3 fracpartial^2 upartial x^2, 0 < x < ?, t > 0 fracpartial upartial x(t, 0) = 0, t ? 0 3. fracpartial upartial x(t, ?) = 0, t ? 0 u(0, x) = x, 0 ? x ? ? fracpartial upartial t = 2 fracpartial^2 upartial x^2, 0 < x < ?, t > 0 4. u(t, 0) = 0, t ? 0 u(t, ?) = 0, t ? 0 u(0, x) = 0, 0 ? x ? ? fracpartial upartial t = 4 fracpartial^2 upartial x^2, 0 < x < ?, t > 0 fracpartial upartial x(t, 0) = 0, t ? 0 5. u(t, ?) = 0, t ? 0 u(0, x) = -?, 0 ? x ? ? 1$

Added by Kelly C.

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