Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question 44 please
![Section 4.3 Auxiliary Equations with Complex Roots
e
y
t
t
t
]
I
44. Solve the initial value problem:
y""-2y"-y' + 2y = 0;
y(0) = 2, y'(0) = 3, y"(0) = 5.
45. By using Newton's method or some other numerical
cedure to approximate the roots of the auxiliary equa
find general solutions to the following equations:
(a) 3y"" + 18y" + 13y' - 19y = 0.
(b) yiv - 5y" + 5y = 0.
(c) yv-3yiv - 5y"" + 15y" + 4y' - 12y = 0.
46. One way to define hyperbolic functions is by mean
differential equations. Consider the equation y" -y
The hyperbolic cosine, cosh t, is defined as the solu
of this equation subject to the initial values: y (0)
and y' (0) = 0. The hyperbolic sine, sinh t, is define](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe38cc688-b545-4be2-9b11-6e87392e9973%2F06b50b14-749e-46bd-a057-31b5b3f3b6b8%2F86xx8x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Section 4.3 Auxiliary Equations with Complex Roots
e
y
t
t
t
]
I
44. Solve the initial value problem:
y""-2y"-y' + 2y = 0;
y(0) = 2, y'(0) = 3, y"(0) = 5.
45. By using Newton's method or some other numerical
cedure to approximate the roots of the auxiliary equa
find general solutions to the following equations:
(a) 3y"" + 18y" + 13y' - 19y = 0.
(b) yiv - 5y" + 5y = 0.
(c) yv-3yiv - 5y"" + 15y" + 4y' - 12y = 0.
46. One way to define hyperbolic functions is by mean
differential equations. Consider the equation y" -y
The hyperbolic cosine, cosh t, is defined as the solu
of this equation subject to the initial values: y (0)
and y' (0) = 0. The hyperbolic sine, sinh t, is define
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