d. y'= 1+y² 1+t² y(0) = -1

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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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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D
2. Separation of Variables
Determine which of the following differential equations are separable. Do not solve the differential
equation; write the separated form if possible.
1. y'= 1 + y
4. y' = In(ty)
7. y' =
9. V =
y'
y+
e.
a.
b. 4tdy= (y² + ty²)dt y(1) = 1
c. y' =
y (2) = 0
2t
1+2y
d. y'=-
2. y' = y - y³
5. y' = d+
Solve the following differential equations by separation of variables:
'=²/²²
1+y²
1+12
y' = tye-t
3. y'= sin(t + y)
y +1
+!
ty
y(0) = -1
6. y' =
8. y =
10. ty' = 1 + y²
ln(y) +1²
Transcribed Image Text:2. Separation of Variables Determine which of the following differential equations are separable. Do not solve the differential equation; write the separated form if possible. 1. y'= 1 + y 4. y' = In(ty) 7. y' = 9. V = y' y+ e. a. b. 4tdy= (y² + ty²)dt y(1) = 1 c. y' = y (2) = 0 2t 1+2y d. y'=- 2. y' = y - y³ 5. y' = d+ Solve the following differential equations by separation of variables: '=²/²² 1+y² 1+12 y' = tye-t 3. y'= sin(t + y) y +1 +! ty y(0) = -1 6. y' = 8. y = 10. ty' = 1 + y² ln(y) +1²
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