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(a) Solve the differential equation y' = x/1- 9y2.

(a) Solve the differential equation y' = x/1- 9y2.

Advanced Engineering Mathematics
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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(c) Does the initial-value problem y' = *V1 - 9y2, y(0) = 3, have a solution? Explain. O For V1 - 9y2 to be a real number, we must have y 2 1/3; that is, y(0) 2 1/3. Thus, the initial-value problem y' = V1- 9y2, y(0) = 3, does not have a solution. O For V1- 9y2 to be a real number, we must have y 2 1/3; that is, y(0) 2 1/3. Thus, the initial-value problem y' =xV1- 9y?, y(0) = 3, does have a solution. O For V1- 9y2 to be a real number, we must have -1/3 s y < 1/3; that is, -1/3 < y(0) < 1/3. Thus, the initial-value problem y' = x/1- 9y2, y(0) = 3, does not have a solution. O For V1 - 9y2 to be a real number, we must have -1/3 sys 1/3; that is, -1/3 s y(0) < 1/3. Thus, the initial-value problem y' = xV1 - 9y², y(0) = 3, does have a solution.
Transcribed Image Text:(c) Does the initial-value problem y' = *V1 - 9y2, y(0) = 3, have a solution? Explain. O For V1 - 9y2 to be a real number, we must have y 2 1/3; that is, y(0) 2 1/3. Thus, the initial-value problem y' = V1- 9y2, y(0) = 3, does not have a solution. O For V1- 9y2 to be a real number, we must have y 2 1/3; that is, y(0) 2 1/3. Thus, the initial-value problem y' =xV1- 9y?, y(0) = 3, does have a solution. O For V1- 9y2 to be a real number, we must have -1/3 s y < 1/3; that is, -1/3 < y(0) < 1/3. Thus, the initial-value problem y' = x/1- 9y2, y(0) = 3, does not have a solution. O For V1 - 9y2 to be a real number, we must have -1/3 sys 1/3; that is, -1/3 s y(0) < 1/3. Thus, the initial-value problem y' = xV1 - 9y², y(0) = 3, does have a solution.
(a) Solve the differential equation y' = (1 - 9y2. (b) Solve the initial-value problem y' = x/1- 9y², y(0) = 0.
Transcribed Image Text:(a) Solve the differential equation y' = (1 - 9y2. (b) Solve the initial-value problem y' = x/1- 9y², y(0) = 0.
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