6. For each of the following first-order differential equations, answer whether it is integ- rable, separable, linear, or neither. (An equation may be several of these at once, in which case write all that apply.) dy (a) + ry = r²y?. dy + ry = e dr dy + sin(x). dy (c) + cos(y) = sin(x). dr (d) + 5t = t sin(x). (e) (1 – t) dr + cos(t)x = e'. dt

Calculus: Early Transcendentals
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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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6. For each of the following first-order differential equations, answer whether it is integ-
rable, separable, linear, or neither. (An equation may be several of these at once, in
which case write all that apply.)
dy
(a)
+ ry = r²y?.
dy
+ ry = e
dr
dy
+ sin(x).
dy
(c)
+ cos(y) = sin(x).
dr
(d)
+ 5t = t sin(x).
(e) (1 – t)
dr
+ cos(t)x = e'.
dt
Transcribed Image Text:6. For each of the following first-order differential equations, answer whether it is integ- rable, separable, linear, or neither. (An equation may be several of these at once, in which case write all that apply.) dy (a) + ry = r²y?. dy + ry = e dr dy + sin(x). dy (c) + cos(y) = sin(x). dr (d) + 5t = t sin(x). (e) (1 – t) dr + cos(t)x = e'. dt
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