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
Question 16 pls
Section 8.5
![tions. As we will see, operator methods similar to those
the desired second solution.
m
on
F5
In Problems 15-17, solve the given initial value problem.
15. t²x"(t) — 12x(t) = 0 ;
x(1) = 3, x' (1) = 5
16. xy"(x) + 5xy' (x) + 4y(x) = 0;
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available until you sign in again.
y (1) = 3, y' (1) = 7
17. x³y" (x) + 6x²y" (x) +29xy' (x) - 29y(x) = 0;
y (1) = 2, y' (1) = -3, y" (1) = 19
I
18. Suppose ro is a repeated root of the auxiliary equation
ar² + br+c= 0. Then, as we well know, y₁ (t) =
erot
is a solution to the equation ay" + by' + cy = 0, where
a, b, and c are constants. Use a derivation similar to the
one given in this section for the case when the indicial
equation has a repeated root to show that a second lin-
early independent solution is y2 (t) = teot.
19. Let L[y] (x)
x³y" (x) + xy' (x) − y(x).
(a) Show that L[x] (x) = (r-1)³x².
(b) Using an extension of the argument given in this
section for the case when the indicial equation
has a double root, show that L[y] = 0 has the
F6
DD](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe38cc688-b545-4be2-9b11-6e87392e9973%2Fe970199c-f005-4d91-9ef7-375a3c3804e4%2F62er7hv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:tions. As we will see, operator methods similar to those
the desired second solution.
m
on
F5
In Problems 15-17, solve the given initial value problem.
15. t²x"(t) — 12x(t) = 0 ;
x(1) = 3, x' (1) = 5
16. xy"(x) + 5xy' (x) + 4y(x) = 0;
Update Apple ID Settings
Some account services will not
available until you sign in again.
y (1) = 3, y' (1) = 7
17. x³y" (x) + 6x²y" (x) +29xy' (x) - 29y(x) = 0;
y (1) = 2, y' (1) = -3, y" (1) = 19
I
18. Suppose ro is a repeated root of the auxiliary equation
ar² + br+c= 0. Then, as we well know, y₁ (t) =
erot
is a solution to the equation ay" + by' + cy = 0, where
a, b, and c are constants. Use a derivation similar to the
one given in this section for the case when the indicial
equation has a repeated root to show that a second lin-
early independent solution is y2 (t) = teot.
19. Let L[y] (x)
x³y" (x) + xy' (x) − y(x).
(a) Show that L[x] (x) = (r-1)³x².
(b) Using an extension of the argument given in this
section for the case when the indicial equation
has a double root, show that L[y] = 0 has the
F6
DD
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