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The direction field for = dx 16y is shown to the right. (a) Verify that the straight lines y = x are solution curves, provided x * 0. (b) Sketch the solution curve with initial condition y(0) = -3. (c) Sketch the solution curve with initial condition y(1) = -1. (d) What can be said about the behavior of the above solutions as x→ +∞o? How about x→ -∞o?

The direction field for = dx 16y is shown to the right. (a) Verify that the straight lines y = x are solution curves, provided x * 0. (b) Sketch the solution curve with initial condition y(0) = -3. (c) Sketch the solution curve with initial condition y(1) = -1. (d) What can be said about the behavior of the above solutions as x→ +∞o? How about x→ -∞o?

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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Question
Please solve for b,c,d
The direction field for = is shown to the right. dy 25x dx 16y 5 ± (a) Verify that the straight lines y = x are solution curves, provided x # 0. (b) Sketch the solution curve with initial condition y(0) = -3. (c) Sketch the solution curve with initial condition y(1) = -1. (d) What can be said about the behavior of the above solutions as x→ + ∞o? How about x→→∞? 5 B. As x→+0o, the solution approaches and has the line y = - x as an asymptote. -∞o O A. As x-∞o, the solution approaches c. The solution does not approach a single value or ± ∞o as X→ +∞0. OD. The solution does not exist for positive x. What can be said about the behavior of the solution in part (b) as x→∞o? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 5 and has the line y = -x as an asymptote. 5 and has the line y=x as an asymptote. B. As x→∞o, the solution approaches Oc. The solution does not approach a single value or ± ∞ as x→-00. C. OD. The solution does not exist for negative x. ID 4 +++
Transcribed Image Text:The direction field for = is shown to the right. dy 25x dx 16y 5 ± (a) Verify that the straight lines y = x are solution curves, provided x # 0. (b) Sketch the solution curve with initial condition y(0) = -3. (c) Sketch the solution curve with initial condition y(1) = -1. (d) What can be said about the behavior of the above solutions as x→ + ∞o? How about x→→∞? 5 B. As x→+0o, the solution approaches and has the line y = - x as an asymptote. -∞o O A. As x-∞o, the solution approaches c. The solution does not approach a single value or ± ∞o as X→ +∞0. OD. The solution does not exist for positive x. What can be said about the behavior of the solution in part (b) as x→∞o? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 5 and has the line y = -x as an asymptote. 5 and has the line y=x as an asymptote. B. As x→∞o, the solution approaches Oc. The solution does not approach a single value or ± ∞ as x→-00. C. OD. The solution does not exist for negative x. ID 4 +++
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