Custom Kreyszig: Advanced Engineering Mathematics
10th Edition
ISBN: 9781119166856
Author: Kreyszig
Publisher: JOHN WILEY+SONS INC.CUSTOM
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Solve the initial value problem:
y' =
x3
+ y³
3
,
y(1) = 2
xy²
y(x) =
Hint: Notice that the equation on the right is
homogeneous and see Homework exercise 23 in
section 1.2 of our textbook to review techniques for
solving homogeneous equations.
Note that we've been given an intial value of the form
y(a) = b where a > 0, so this only determines a
solution corresponding to the right half of the graph of
In(x), i.e., the part of the graph corresponding to
positive values of x. Therefore, we should write In(x)
instead of ln(|x|), since the left half of the graph is
not determined by the initial condition given.
Chapter 9 Solutions
Custom Kreyszig: Advanced Engineering Mathematics
Ch. 9.1 - Prob. 1PCh. 9.1 - Find the components of the vector v with initial...Ch. 9.1 - Prob. 3PCh. 9.1 - Prob. 4PCh. 9.1 - Find the components of the vector v with initial...Ch. 9.1 - Find the terminal point Q of the vector v with...Ch. 9.1 - Find the terminal point Q of the vector v with...Ch. 9.1 - Find the terminal point Q of the vector v with...Ch. 9.1 - Find the terminal point Q of the vector v with...Ch. 9.1 - Find the terminal point Q of the vector v with...
Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Prob. 13PCh. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - Prob. 17PCh. 9.1 - Let a = [3, 2, 0] = 3i + 2j; b = [−4, 6, 0] = 4i +...Ch. 9.1 - What laws do Probs. 12–16 illustrate?
12. (a + b)...Ch. 9.1 - Prob. 20PCh. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Prob. 22PCh. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Find the resultant in terms of components and its...Ch. 9.1 - Equilibrium. Find v such that p, q, u in Prob. 21...Ch. 9.1 - Find p such that u, v, w in Prob. 23 and p are in...Ch. 9.1 - Unit vector. Find the unit vector in the direction...Ch. 9.1 - Restricted resultant. Find all v such that the...Ch. 9.1 - Prob. 30PCh. 9.1 - For what k is the resultant of [2, 0, −7], [1, 2,...Ch. 9.1 - If |p| = 6 and |q| = 4, what can you say about the...Ch. 9.1 - Same question as in Prob. 32 if |p| = 9, |q| = 6,...Ch. 9.1 - Relative velocity. If airplanes A and B are moving...Ch. 9.1 - Same question as in Prob. 34 for two ships moving...Ch. 9.1 - Prob. 36PCh. 9.1 - Prob. 37PCh. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Prob. 8PCh. 9.2 - Prob. 9PCh. 9.2 - Let a = [1, −3, 5], b = [4, 0, 8], c = [−2, 9, 1]....Ch. 9.2 - Prob. 11PCh. 9.2 - What does u • v = u • w imply if u = 0? If u ≠...Ch. 9.2 - Prove the Cauchy–Schwarz inequality.
Ch. 9.2 - Verify the Cauchy–Schwarz and triangle...Ch. 9.2 - Prob. 15PCh. 9.2 - Triangle inequality. Prove Eq. (7). Hint. Use Eq....Ch. 9.2 - Prob. 17PCh. 9.2 - Prob. 18PCh. 9.2 - Prob. 19PCh. 9.2 - Prob. 20PCh. 9.2 - Prob. 21PCh. 9.2 - Let a = [1, 1, 0], b = [3, 2, 1], and c = [1, 0,...Ch. 9.2 - Let a = [1, 1, 0], b = [3, 2, 1], and c = [1, 0,...Ch. 9.2 - Let a = [1, 1, 0], b = [3, 2, 1], and c = [1, 0,...Ch. 9.2 - What will happen to the angle in Prob. 24 if we...Ch. 9.2 - Prob. 26PCh. 9.2 - Addition law. cos (α − β) = cos α cos β + sin α...Ch. 9.2 - Prob. 28PCh. 9.2 - Prob. 29PCh. 9.2 - Prob. 30PCh. 9.2 - Prob. 31PCh. 9.2 - Prob. 32PCh. 9.2 - Prob. 33PCh. 9.2 - Prob. 34PCh. 9.2 - Prob. 35PCh. 9.2 - Prob. 36PCh. 9.2 - Prob. 37PCh. 9.2 - Prob. 38PCh. 9.2 - Prob. 39PCh. 9.2 - Prob. 40PCh. 9.3 - Prob. 1PCh. 9.3 - Prob. 2PCh. 9.3 - Prob. 3PCh. 9.3 - Prob. 4PCh. 9.3 - Prob. 5PCh. 9.3 - Prob. 6PCh. 9.3 - Prob. 7PCh. 9.3 - Prob. 8PCh. 9.3 - Prob. 9PCh. 9.3 - Prob. 11PCh. 9.3 - Prob. 12PCh. 9.3 - Prob. 13PCh. 9.3 - Prob. 14PCh. 9.3 - Prob. 15PCh. 9.3 - Prob. 16PCh. 9.3 - Prob. 17PCh. 9.3 - Prob. 18PCh. 9.3 - Prob. 19PCh. 9.3 - Prob. 20PCh. 9.3 - Prob. 21PCh. 9.3 - Prob. 22PCh. 9.3 - Prob. 23PCh. 9.3 - Prob. 25PCh. 9.3 - Prob. 26PCh. 9.3 - Prob. 27PCh. 9.3 - Prob. 28PCh. 9.3 - Prob. 29PCh. 9.3 - Prob. 30PCh. 9.3 - Prob. 31PCh. 9.3 - Prob. 32PCh. 9.3 - Prob. 33PCh. 9.3 - Prob. 34PCh. 9.4 - Prob. 1PCh. 9.4 - Prob. 2PCh. 9.4 - Prob. 3PCh. 9.4 - Prob. 4PCh. 9.4 - Prob. 5PCh. 9.4 - Prob. 6PCh. 9.4 - Prob. 7PCh. 9.4 - Prob. 9PCh. 9.4 - Prob. 10PCh. 9.4 - Prob. 11PCh. 9.4 - Prob. 12PCh. 9.4 - Prob. 13PCh. 9.4 - Prob. 14PCh. 9.4 - Prob. 15PCh. 9.4 - Prob. 16PCh. 9.4 - Prob. 17PCh. 9.4 - Prob. 18PCh. 9.4 - Prob. 19PCh. 9.4 - Prob. 20PCh. 9.4 - Prob. 22PCh. 9.4 - Prob. 23PCh. 9.4 - Prob. 24PCh. 9.5 - Prob. 1PCh. 9.5 - Prob. 2PCh. 9.5 - Prob. 3PCh. 9.5 - Prob. 4PCh. 9.5 - Prob. 5PCh. 9.5 - Prob. 6PCh. 9.5 - Prob. 7PCh. 9.5 - Prob. 8PCh. 9.5 - Prob. 9PCh. 9.5 - Prob. 10PCh. 9.5 - Prob. 11PCh. 9.5 - Prob. 12PCh. 9.5 - Prob. 13PCh. 9.5 - Prob. 14PCh. 9.5 - Prob. 15PCh. 9.5 - Prob. 16PCh. 9.5 - Prob. 17PCh. 9.5 - Prob. 18PCh. 9.5 - Prob. 19PCh. 9.5 - Prob. 20PCh. 9.5 - Prob. 21PCh. 9.5 - r(t) = [10 cos t, 1, 10 sin t], P: (6, 1, 8)Ch. 9.5 - r(t) = [cos t, sin t, 9t], P: (1, 0, 18)Ch. 9.5 - Prob. 27PCh. 9.5 - Prob. 29PCh. 9.5 - Prob. 30PCh. 9.5 - Prob. 31PCh. 9.5 - Prob. 32PCh. 9.5 - Prob. 33PCh. 9.5 - Prob. 34PCh. 9.5 - Prob. 35PCh. 9.5 - Prob. 36PCh. 9.5 - Prob. 37PCh. 9.5 - Prob. 38PCh. 9.5 - Prob. 43PCh. 9.5 - Prob. 44PCh. 9.5 - Prob. 45PCh. 9.5 - Prob. 46PCh. 9.5 - CURVATURE AND TORSION
47. Circle. Show that a...Ch. 9.5 - Prob. 48PCh. 9.5 - Prob. 49PCh. 9.5 - Prob. 50PCh. 9.5 - Prob. 51PCh. 9.5 - Prob. 52PCh. 9.5 - Prob. 53PCh. 9.5 - Prob. 54PCh. 9.5 - Prob. 55PCh. 9.7 - Prob. 1PCh. 9.7 - Prob. 2PCh. 9.7 - Prob. 3PCh. 9.7 - Prob. 4PCh. 9.7 - Prob. 5PCh. 9.7 - Prob. 6PCh. 9.7 - Prob. 7PCh. 9.7 - Prob. 8PCh. 9.7 - Prob. 9PCh. 9.7 - Prob. 10PCh. 9.7 - Prob. 11PCh. 9.7 - Prob. 12PCh. 9.7 - Prob. 13PCh. 9.7 - Prob. 14PCh. 9.7 - Prob. 15PCh. 9.7 - Prob. 16PCh. 9.7 - Prob. 17PCh. 9.7 - Prob. 18PCh. 9.7 - Prob. 19PCh. 9.7 - Prob. 20PCh. 9.7 - Prob. 21PCh. 9.7 - Prob. 22PCh. 9.7 - Prob. 23PCh. 9.7 - Prob. 24PCh. 9.7 - Prob. 25PCh. 9.7 - Prob. 26PCh. 9.7 - Prob. 28PCh. 9.7 - Prob. 29PCh. 9.8 - Prob. 1PCh. 9.8 - Prob. 2PCh. 9.8 - Prob. 3PCh. 9.8 - Prob. 4PCh. 9.8 - Prob. 5PCh. 9.8 - Prob. 6PCh. 9.8 - Prob. 7PCh. 9.8 - Prob. 8PCh. 9.8 - CAS EXPERIMENT. Visualizing the Divergence. Graph...Ch. 9.8 - Prob. 11PCh. 9.8 - Prob. 12PCh. 9.8 - Prob. 13PCh. 9.8 - Prob. 14PCh. 9.8 - Prob. 15PCh. 9.8 - Prob. 16PCh. 9.8 - Prob. 17PCh. 9.8 - Prob. 18PCh. 9.8 - Prob. 19PCh. 9.8 - Prob. 20PCh. 9.9 - Prob. 1PCh. 9.9 - Prob. 2PCh. 9.9 - Prob. 3PCh. 9.9 - Prob. 4PCh. 9.9 - Prob. 5PCh. 9.9 - Prob. 6PCh. 9.9 - Prob. 7PCh. 9.9 - Prob. 8PCh. 9.9 - Prob. 9PCh. 9.9 - Prob. 10PCh. 9.9 - Prob. 11PCh. 9.9 - Prob. 12PCh. 9.9 - Prob. 13PCh. 9.9 - Prob. 15PCh. 9.9 - Prob. 16PCh. 9.9 - Prob. 17PCh. 9.9 - Prob. 18PCh. 9.9 - Prob. 19PCh. 9.9 - Prob. 20PCh. 9 - Prob. 1RQCh. 9 - Prob. 2RQCh. 9 - Prob. 3RQCh. 9 - Prob. 4RQCh. 9 - Prob. 5RQCh. 9 - Prob. 6RQCh. 9 - Prob. 7RQCh. 9 - Prob. 8RQCh. 9 - Prob. 9RQCh. 9 - Prob. 11RQCh. 9 - Prob. 12RQCh. 9 - Prob. 13RQCh. 9 - Prob. 14RQCh. 9 - Prob. 15RQCh. 9 - Prob. 16RQCh. 9 - Prob. 17RQCh. 9 - Prob. 18RQCh. 9 - Prob. 19RQCh. 9 - Prob. 20RQCh. 9 - Prob. 21RQCh. 9 - Prob. 22RQCh. 9 - Prob. 23RQCh. 9 - Prob. 24RQCh. 9 - Prob. 25RQCh. 9 - Prob. 26RQCh. 9 - Prob. 27RQCh. 9 - Prob. 28RQCh. 9 - Prob. 29RQCh. 9 - Prob. 30RQCh. 9 - Prob. 31RQCh. 9 - Prob. 32RQCh. 9 - Prob. 33RQCh. 9 - Prob. 34RQCh. 9 - Prob. 35RQCh. 9 - Prob. 36RQCh. 9 - Prob. 37RQCh. 9 - Prob. 38RQCh. 9 - Prob. 39RQCh. 9 - Prob. 40RQ
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