Fundamentals of Differential Equations (9th Edition)
9th Edition
ISBN: 9780321977069
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
Publisher: PEARSON
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EXAMPLE 3
Find
S
X
√√2-2x2
dx.
SOLUTION Let u = 2 - 2x². Then du =
Χ
dx =
2- 2x²
=
信
du
dx, so x dx =
du and
u-1/2 du
(2√u) + C
+ C (in terms of x).
Let g(z) =
z-i
z+i'
(a) Evaluate g(i) and g(1).
(b) Evaluate the limits
lim g(z), and lim g(z).
2-12
(c) Find the image of the real axis under g.
(d) Find the image of the upper half plane {z: Iz > 0} under the function g.
k
(i) Evaluate
k=7
k=0
[Hint: geometric series + De Moivre]
(ii) Find an upper bound for the expression
1
+2x+2
where z lies on the circle || z|| = R with R > 10. [Hint: Use Cauchy-Schwarz]
Chapter 2 Solutions
Fundamentals of Differential Equations (9th Edition)
Ch. 2.2 - In Problems 16, determine whether the given...Ch. 2.2 - In Problems 16, determine whether the given...Ch. 2.2 - In Problems 16, determine whether the given...Ch. 2.2 - In Problems 16, determine whether the given...Ch. 2.2 - In Problems 16, determine whether the given...Ch. 2.2 - In Problems 16, determine whether the given...Ch. 2.2 - In Problems 716, solve the equation. 7. xdydx=1y3Ch. 2.2 - In Problems 716, solve the equation. 8. dxdt=3xt2Ch. 2.2 - In Problems 716, solve the equation. 9....Ch. 2.2 - In Problems 716, solve the equation. 10....
Ch. 2.2 - In Problems 716, solve the equation. 11....Ch. 2.2 - In Problems 716, solve the equation. 12....Ch. 2.2 - In Problems 716, solve the equation. 13....Ch. 2.2 - In Problems 716, solve the equation. 14. dxdtx3=xCh. 2.2 - In Problems 716, solve the equation. 15....Ch. 2.2 - In Problems 716, solve the equation. 16. y1 dy +...Ch. 2.2 - In Problems 1726, solve the initial value problem....Ch. 2.2 - In Problems 1726, solve the initial value problem....Ch. 2.2 - In Problems 1726, solve the initial value problem....Ch. 2.2 - In Problems 1726, solve the initial value problem....Ch. 2.2 - In Problems 1726, solve the initial value problem....Ch. 2.2 - In Problems 1726, solve the initial value problem....Ch. 2.2 - Prob. 23ECh. 2.2 - In Problems 1726, solve the initial value problem....Ch. 2.2 - In Problems 1726, solve the initial value problem....Ch. 2.2 - In Problems 1726, solve the initial value problem....Ch. 2.2 - Prob. 27ECh. 2.2 - Sketch the solution to the initial value problem...Ch. 2.2 - Uniqueness Questions. In Chapter 1 we indicated...Ch. 2.2 - As stated in this section, the separation of...Ch. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - Mixing. Suppose a brine containing 0.3 kilogram...Ch. 2.2 - Newtons Law of Cooling. According to Newtons law...Ch. 2.2 - Prob. 35ECh. 2.2 - Prob. 36ECh. 2.2 - Compound Interest. If P(t) is the amount of...Ch. 2.2 - Free Fall. In Section 2.1, we discussed a model...Ch. 2.2 - Grand Prix Race. Driver A had been leading...Ch. 2.2 - Prob. 40ECh. 2.3 - In Problems 16, determine whether the given...Ch. 2.3 - In Problems 16, determine whether the given...Ch. 2.3 - In Problems 16, determine whether the given...Ch. 2.3 - In Problems 16, determine whether the given...Ch. 2.3 - In Problems 16, determine whether the given...Ch. 2.3 - In Problems 16, determine whether the given...Ch. 2.3 - In Problems 716, obtain the general solution to...Ch. 2.3 - In Problems 716, obtain the general solution to...Ch. 2.3 - In Problems 716, obtain the general solution to...Ch. 2.3 - In Problems 716, obtain the general solution to...Ch. 2.3 - In Problems 716, obtain the general solution to...Ch. 2.3 - In Problems 716, obtain the general solution to...Ch. 2.3 - In Problems 716, obtain the general solution to...Ch. 2.3 - In Problems 716, obtain the general solution to...Ch. 2.3 - Prob. 15ECh. 2.3 - Prob. 17ECh. 2.3 - Prob. 18ECh. 2.3 - Prob. 19ECh. 2.3 - Prob. 20ECh. 2.3 - In Problems 1722, solve the initial value problem....Ch. 2.3 - In Problems 1722, solve the initial value problem....Ch. 2.3 - Radioactive Decay. In Example 2 assume that the...Ch. 2.3 - Prob. 24ECh. 2.3 - (a) Using definite integration, show that the...Ch. 2.3 - Prob. 26ECh. 2.3 - Constant Multiples of Solutions. (a) Show that y =...Ch. 2.3 - Prob. 29ECh. 2.3 - Bernoulli Equations. The equation (18) dydx+2y=xy2...Ch. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 36ECh. 2.3 - Prob. 37ECh. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.4 - In Problems 18, classify the equation as...Ch. 2.4 - In Problems 18, classify the equation as...Ch. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - In Problems 18, classify the equation as...Ch. 2.4 - In Problems 18, classify the equation as...Ch. 2.4 - In Problems 18, classify the equation as...Ch. 2.4 - In Problems 18, classify the equation as...Ch. 2.4 - Prob. 9ECh. 2.4 - In Problems 920, determine whether the equation is...Ch. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - In Problems 920, determine whether the equation is...Ch. 2.4 - Prob. 15ECh. 2.4 - In Problems 920, determine whether the equation is...Ch. 2.4 - Prob. 17ECh. 2.4 - In Problems 920, determine whether the equation is...Ch. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - In Problems 2126, solve the initial value problem....Ch. 2.4 - Prob. 22ECh. 2.4 - Prob. 23ECh. 2.4 - In Problems 2126, solve the initial value problem....Ch. 2.4 - Prob. 25ECh. 2.4 - In Problems 2126, solve the initial value problem....Ch. 2.4 - Prob. 27ECh. 2.4 - For each of the following equations, find the most...Ch. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Orthogonal Trajectories. A geometric problem...Ch. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.5 - Prob. 1ECh. 2.5 - In Problems 16, identify the equation as...Ch. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - In Problems 16, identify the equation as...Ch. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - Prob. 10ECh. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Verify that when the linear differential equation...Ch. 2.6 - In Problems 18, identify (do not solve) the...Ch. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Prob. 4ECh. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - In Problems 18, identify (do not solve) the...Ch. 2.6 - Prob. 8ECh. 2.6 - Use the method discussed under Homogeneous...Ch. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - Prob. 12ECh. 2.6 - Prob. 13ECh. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Prob. 16ECh. 2.6 - Prob. 17ECh. 2.6 - Prob. 18ECh. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - Use the method discussed under Bernoulli Equations...Ch. 2.6 - Prob. 24ECh. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Use the method discussed under Equations with...Ch. 2.6 - Prob. 30ECh. 2.6 - Prob. 31ECh. 2.6 - Prob. 32ECh. 2.6 - Prob. 33ECh. 2.6 - Prob. 34ECh. 2.6 - Prob. 35ECh. 2.6 - In Problems 3340, solve the equation given in: 36....Ch. 2.6 - Prob. 37ECh. 2.6 - Prob. 38ECh. 2.6 - Prob. 39ECh. 2.6 - Prob. 40ECh. 2.6 - Prob. 41ECh. 2.6 - Prob. 42ECh. 2.6 - Prob. 43ECh. 2.6 - Show that equation (13) reduces to an equation of...Ch. 2.6 - Prob. 45ECh. 2.6 - Prob. 46ECh. 2.6 - Prob. 47ECh. 2.6 - Prob. 48ECh. 2 - In Problems 130, solve the equation. 1....Ch. 2 - Prob. 2RPCh. 2 - Prob. 3RPCh. 2 - Prob. 4RPCh. 2 - Prob. 5RPCh. 2 - In Problems 130, solve the equation. 6. 2xy3 dx ...Ch. 2 - In Problems 130, solve the equation. 7. t3y2 dt +...Ch. 2 - Prob. 8RPCh. 2 - In Problems 130, solve the equation. 9. (x2 + y2)...Ch. 2 - Prob. 10RPCh. 2 - Prob. 11RPCh. 2 - Prob. 12RPCh. 2 - Prob. 13RPCh. 2 - Prob. 14RPCh. 2 - Prob. 15RPCh. 2 - Prob. 16RPCh. 2 - Prob. 17RPCh. 2 - Prob. 18RPCh. 2 - Prob. 19RPCh. 2 - Prob. 20RPCh. 2 - Prob. 21RPCh. 2 - Prob. 22RPCh. 2 - Prob. 23RPCh. 2 - In Problems 130, solve the equation. 24. (y/x +...Ch. 2 - Prob. 25RPCh. 2 - Prob. 26RPCh. 2 - Prob. 27RPCh. 2 - Prob. 28RPCh. 2 - Prob. 29RPCh. 2 - Prob. 30RPCh. 2 - Prob. 31RPCh. 2 - Prob. 32RPCh. 2 - Prob. 33RPCh. 2 - Prob. 34RPCh. 2 - Prob. 35RPCh. 2 - Prob. 36RPCh. 2 - Prob. 37RPCh. 2 - Prob. 38RPCh. 2 - Prob. 39RPCh. 2 - Prob. 40RPCh. 2 - Prob. 41RP
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