Consider the differential equation y'= y² where y is considered to be a function of x. In this exercise, you will determine whether or not 1 is a solution to the differential equation Y 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'. y' = (b) Next substitute the above expression for y into the right side of the differential equation. In other words, compute y². y² (c) Based on your answers to (a) and (b) can we say

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the differential equation
y'= y²
where Y is considered to be a function of x.
In this exercise, you will determine whether or not
1
Y
=
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'.
y' =
(b) Next substitute the above expression for y into
the right side of the differential equation. In other
words, compute y².
y²
is a solution to the differential equation
(c) Based on your answers to (a) and (b), can we say
1
that
y =
equation?
Yes
No
x + c
is a solution to the differential
Transcribed Image Text:Consider the differential equation y'= y² where Y is considered to be a function of x. In this exercise, you will determine whether or not 1 Y = 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'. y' = (b) Next substitute the above expression for y into the right side of the differential equation. In other words, compute y². y² is a solution to the differential equation (c) Based on your answers to (a) and (b), can we say 1 that y = equation? Yes No x + c is a solution to the differential
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