Consider the differential equation y" = ef + xy' where y is considered to be a function of . In this exercise, you will determine whether or not y = e + c is a solution to the differential equation 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 e + xy'. (c) Based on your answers to (a) and (b), can we say that y = eT is a solution to the differential equation? O No O Yes
Consider the differential equation y" = ef + xy' where y is considered to be a function of . In this exercise, you will determine whether or not y = e + c is a solution to the differential equation 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 e + xy'. (c) Based on your answers to (a) and (b), can we say that y = eT is a solution to the differential equation? O No O Yes
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
![Consider the differential equation
y'' = ei + xy'
where y is considered to be a function of .
2
In this exercise, you will determine whether or not y = e + c is a solution to the differential equation
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 e² + xy'.
z2
(c) Based on your answers to (a) and (b), can we say that y = eT is a solution to the differential
equation?
O No
O Yes
O M
B
#3
CA
$
4
%
5
Oll
6
&
7
O
*
8
9](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe727a2e-7f05-4f92-9309-f9684914a58d%2Fefe4a4dd-026b-4235-9159-9c2b3cf42a31%2Fa2bf3id_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the differential equation
y'' = ei + xy'
where y is considered to be a function of .
2
In this exercise, you will determine whether or not y = e + c is a solution to the differential equation
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 e² + xy'.
z2
(c) Based on your answers to (a) and (b), can we say that y = eT is a solution to the differential
equation?
O No
O Yes
O M
B
#3
CA
$
4
%
5
Oll
6
&
7
O
*
8
9
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