Differential Equations with Boundary-Value Problems
9th Edition
ISBN: 9781337632515
Author: Dennis G. Zill
Publisher: Cengage Learning US
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Chapter 13, Problem 8RE
To determine
To show: The given equation
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1. One of the partial fractions for
2
4x²+x-9
x3+2x²-3x
2
x+1
a) x23 b) x 1½ c) x² d)
x-1
x
is
1. One of the partial fractions for
2
2
4x²+x-9
x3+2x²-3x
a) x3 b) x11 c) x² d) z
x-1
2. Identify the improper integral.
1 x
2 x
dx
a) 3x dx b) f² 3x dx
0 3-2x
0 3-2x
x
is
c) √2^:
4
√232x dx d) fo² 3x dx
1 1
0 3-2x
B. So eax dx converges to
if
:
a) O if a0 c) - 1½ ifa 0
Complete the square and find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the
constant of integration.)
dx
x²-12x+27
Chapter 13 Solutions
Differential Equations with Boundary-Value Problems
Ch. 13.1 - In Problems 1 4 find the steady-state temperature...Ch. 13.1 - In Problems 1 4 find the steady-state temperature...Ch. 13.1 - In Problems 1– 4 find the steady-state temperature...Ch. 13.1 - In Problems 1 4 find the steady-state temperature...Ch. 13.1 - Solve the exterior Dirichlet problem for a...Ch. 13.1 - Find the steady-state temperature u(r, θ) in a...Ch. 13.1 - Find the steady-state temperature u(r, θ) in a...Ch. 13.1 - Find the steady-state temperature u(r, θ) in the...Ch. 13.1 - Find the steady-state temperature u(r, ) in the...Ch. 13.1 - Find the steady-state temperature u(r, ) in the...
Ch. 13.1 - Find the steady-state temperature u(r, ) in the...Ch. 13.1 - If the boundary conditions for the annular plate...Ch. 13.1 - Find the steady-state temperature u(r, θ) in the...Ch. 13.1 - Find the steady-state temperature u(r, θ) in the...Ch. 13.1 - Find the steady-state temperature u(r, ) in the...Ch. 13.1 - Prob. 16ECh. 13.1 - Find the steady-state temperature u(r, ) in the...Ch. 13.1 - The plate in the first quadrant shown in Figure...Ch. 13.1 - Consider the annular plate in Figure 13.1.7....Ch. 13.1 - Prob. 20ECh. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.2 - Find the displacement u(r, t) in Example 1 if f...Ch. 13.2 - A circular membrane of unit radius 1 is clamped...Ch. 13.2 - Find the steady-state temperature u(r, z) in the...Ch. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.2 - Find the steady-state temperature u(r, z) in the...Ch. 13.2 - Find the steady-state temperatures u(r, z) in the...Ch. 13.2 - Find the steady-state temperatures u(r, z) in the...Ch. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - When there is heat transfer from the lateral side...Ch. 13.2 - Find the steady-state temperature u(r, z) in a...Ch. 13.2 - A circular plate is a composite of two different...Ch. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - In this problem we consider the general casethat...Ch. 13.3 - Solve the BVP in Example 1 if f()={50,0/20,/2....Ch. 13.3 - Prob. 2ECh. 13.3 - Prob. 3ECh. 13.3 - Prob. 4ECh. 13.3 - Find the steady-state temperature u(r, ) within a...Ch. 13.3 - The steady-state temperature in a hemisphere of...Ch. 13.3 - Prob. 7ECh. 13.3 - Prob. 8ECh. 13.3 - Prob. 9ECh. 13.3 - Prob. 10ECh. 13.3 - Prob. 11ECh. 13.3 - Prob. 12ECh. 13.3 - Prob. 13ECh. 13 - Find the steady-state temperature u(r, θ) in a...Ch. 13 - Find the steady-state temperature in the circular...Ch. 13 - Prob. 3RECh. 13 - Prob. 4RECh. 13 - Find the steady-state temperature u(r, ) in the...Ch. 13 - Prob. 6RECh. 13 - Prob. 7RECh. 13 - Prob. 8RECh. 13 - Find the steady-state temperature u(r, z) in the...Ch. 13 - Prob. 10RECh. 13 - Find the steady-state temperature u(r, θ) in a...Ch. 13 - Prob. 12RECh. 13 - Prob. 13RECh. 13 - Prob. 14RECh. 13 - Prob. 15RECh. 13 - Find the steady-state temperature u(r, θ) in the...Ch. 13 - Find the steady-state temperature u(r, z) in a...Ch. 13 - Prob. 18RECh. 13 - Prob. 19RECh. 13 - Prob. 20RECh. 13 - Prob. 21RE
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