Consider the differential equation y' = y² where y is considered to be a function of . 1 In this exercise, you will determine whether or not y = is a solution to the differential equation x + c for any constant c. (a) First substitute the above expression for y into the left side of the differential equation. In other words, compute y'. (b) Next substitute the above expression for y into the right side of the differential equation. In other words, compute y². 1 (c) Based on your answers to (a) and (b), can we say that y - is a solution to the differential x + c equation? O Yes O No M B

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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Consider the differential equation
y' = y²
where y is considered to be a function of .
1
In this exercise, you will determine whether or not y =
is a solution to the differential equation
x + c
for any constant c.
(a) First substitute the above expression for y into the left side of the differential equation. In other
words, compute y'.
(b) Next substitute the above expression for y into the right side of the differential equation. In other
words, compute y².
1
(c) Based on your answers to (a) and (b), can we say that y
is a solution to the differential
x + c
equation?
O Yes
O No
Oll
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Transcribed Image Text:Consider the differential equation y' = y² where y is considered to be a function of . 1 In this exercise, you will determine whether or not y = is a solution to the differential equation x + c for any constant c. (a) First substitute the above expression for y into the left side of the differential equation. In other words, compute y'. (b) Next substitute the above expression for y into the right side of the differential equation. In other words, compute y². 1 (c) Based on your answers to (a) and (b), can we say that y is a solution to the differential x + c equation? O Yes O No Oll → #3 3 с $ 4 % 5 6 & 7 O * 8 ( 9
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