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1. The function y =0 is always a solution to a linear homogeneous OD 2. The ODE -(z+y+5) is separable.

1. The function y =0 is always a solution to a linear homogeneous OD 2. The ODE -(z+y+5) is separable.

Calculus: Early Transcendentals
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.
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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