Differential Equations with Boundary-Value Problems (MindTap Course List)
9th Edition
ISBN: 9781305965799
Author: Dennis G. Zill
Publisher: Cengage Learning
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Chapter A, Problem 51E
To determine
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(b) Let I[y] be a functional of y(x) defined by
[[y] = √(x²y' + 2xyy' + 2xy + y²) dr,
subject to boundary conditions
y(0) = 0,
y(1) = 1.
State the Euler-Lagrange equation for finding extreme values of I [y] for this prob-
lem. Explain why the function y(x) = x is an extremal, and for this function,
show that I = 2. Without doing further calculations, give the values of I for the
functions y(x) = x² and y(x) = x³.
Please use mathematical induction to prove this
In simplest terms, Sketch the graph of the parabola. Then, determine its equation.
opens downward, vertex is (- 4, 7), passes through point (0, - 39)
Chapter A Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
Ch. A - Prob. 1ECh. A - In Problems 1 and 2 evaluate the given...Ch. A - Prob. 3ECh. A - Prob. 4ECh. A - In Problems 3–6 use (7) and the known value to...Ch. A - In Problems 3–6 use (7) and the known value to...Ch. A - In Problems 710 use (13) and the known value...Ch. A - Prob. 8ECh. A - Prob. 9ECh. A - Prob. 10E
Ch. A - Prob. 11ECh. A - Prob. 12ECh. A - Prob. 13ECh. A - Prob. 14ECh. A - Prob. 15ECh. A - Prob. 16ECh. A - Prob. 17ECh. A - Prob. 18ECh. A - Prob. 19ECh. A - Prob. 20ECh. A - Prob. 21ECh. A - Prob. 22ECh. A - Prob. 23ECh. A - Prob. 24ECh. A - Prob. 25ECh. A - Prob. 26ECh. A - For x > 0 the gamma function possesses derivatives...Ch. A - Prob. 28ECh. A - Prob. 29ECh. A - Prob. 30ECh. A - Prob. 31ECh. A - Prob. 32ECh. A - Prob. 33ECh. A - Prob. 34ECh. A - Prob. 35ECh. A - Prob. 36ECh. A - Prob. 37ECh. A - Prob. 38ECh. A - Prob. 39ECh. A - Prob. 40ECh. A - Prob. 41ECh. A - Prob. 42ECh. A - Prob. 43ECh. A - Prob. 44ECh. A - Prob. 45ECh. A - Prob. 46ECh. A - Prob. 47ECh. A - Prob. 48ECh. A - Prob. 49ECh. A - Prob. 50ECh. A - Prob. 51ECh. A - Prob. 52ECh. A - Prob. 53ECh. A - Prob. 54ECh. A - Prob. 55ECh. A - Prob. 56E
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- In simplest way, For each quadratic relation, find the zeros and the maximum or minimum. a) y = x 2 + 16 x + 39 b) y = 5 x2 - 50 x - 120arrow_forwardIn simplest terms and step by step Write each quadratic relation in standard form, then fi nd the zeros. y = - 4( x + 6)2 + 36arrow_forwardIn simplest terms and step by step For each quadratic relation, find the zeros and the maximum or minimum. 1) y = - 2 x2 - 28 x + 64 2) y = 6 x2 + 36 x - 42arrow_forward
- Write each relation in standard form a)y = 5(x + 10)2 + 7 b)y = 9(x - 8)2 - 4arrow_forwardIn simplest form and step by step Write the quadratic relation in standard form, then fi nd the zeros. y = 3(x - 1)2 - 147arrow_forwardStep by step instructions The path of a soccer ball can be modelled by the relation h = - 0.1 d 2 + 0.5 d + 0.6, where h is the ball’s height and d is the horizontal distance from the kicker. a) Find the zeros of the relation.arrow_forward
- In simplest terms, Describe the shape and position of the parabola relative to the graph of y = x 2 y = - 80( x + 9) 2 + 10.8arrow_forwardas a Identify each equation Parabola, circle, ellipse perbola without completio the square. x²-6x-14 y = 33-y² 14y ofarrow_forwardI need the last answer t=? I did got the answer for the first two this is just homework.arrow_forward
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