Which of the following functions (there may be more than one) are particular solutions to the differential equation: y'' 8y' + 16y= 7t + 4 - y = Y = 7 Oy= -t + 16 8t + 15 32 4t Y = e¹t (1+t) = sin(t) 15 32
Which of the following functions (there may be more than one) are particular solutions to the differential equation: y'' 8y' + 16y= 7t + 4 - y = Y = 7 Oy= -t + 16 8t + 15 32 4t Y = e¹t (1+t) = sin(t) 15 32
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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![The problem asks which of the following functions are particular solutions to the differential equation:
\[ y'' - 8y' + 16y = 7t + 4 \]
The functions provided as options are:
1. \[ y = \frac{7}{16} t + \frac{15}{32} \]
2. \[ y = 8t + \frac{15}{32} \]
3. \[ y = e^{4t}(1 + t) \]
4. \[ y = \sin(t) \]
To determine which functions solve the differential equation, substitute each function into the equation and check if they satisfy it.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b115b68-3600-4afc-99cf-4f7f40f83514%2Ffaeb055a-efaf-4f34-b1bf-44970210c332%2F19ec9fr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The problem asks which of the following functions are particular solutions to the differential equation:
\[ y'' - 8y' + 16y = 7t + 4 \]
The functions provided as options are:
1. \[ y = \frac{7}{16} t + \frac{15}{32} \]
2. \[ y = 8t + \frac{15}{32} \]
3. \[ y = e^{4t}(1 + t) \]
4. \[ y = \sin(t) \]
To determine which functions solve the differential equation, substitute each function into the equation and check if they satisfy it.
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