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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![O': Answer only True/False .for each in the following
1. The function y 0 is always a solution to a linear homogenecus OD.
-(x+++5)* is separable.
2. The ODE
3. If y(a) is a solution to an.ODE and contains a arbitrary constants, then it must be
the general solution to th ODE.
4. A first-order ODE can never be linear, separable, and exact at the same time.
5. The ODE y- e-79 is separable.
6. The ODE M(s,9) dz + N(a, 9) dy = 0 is exact if and only if M(s.y) ON(2,9)
7. For any linear ODE, the sum of any two sohations is also a solution.
8. The only particular solution to a second-order linear homogeneous ODE is the zero
solution.
9. The ODE
form y-z" for some constant r.
- 3y = 0 is a Cauchy-Euler equation and has one solution of the
10. The function e" is an integrating factor for the ODE y-2ry z.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9358c98a-9695-44da-ba98-84956426dfeb%2F70b7a8a7-ae76-4426-b942-e14060851eea%2F78d7xls_processed.jpeg&w=3840&q=75)
Transcribed Image Text:O': Answer only True/False .for each in the following
1. The function y 0 is always a solution to a linear homogenecus OD.
-(x+++5)* is separable.
2. The ODE
3. If y(a) is a solution to an.ODE and contains a arbitrary constants, then it must be
the general solution to th ODE.
4. A first-order ODE can never be linear, separable, and exact at the same time.
5. The ODE y- e-79 is separable.
6. The ODE M(s,9) dz + N(a, 9) dy = 0 is exact if and only if M(s.y) ON(2,9)
7. For any linear ODE, the sum of any two sohations is also a solution.
8. The only particular solution to a second-order linear homogeneous ODE is the zero
solution.
9. The ODE
form y-z" for some constant r.
- 3y = 0 is a Cauchy-Euler equation and has one solution of the
10. The function e" is an integrating factor for the ODE y-2ry z.
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