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3. Consider the DE 4 = 2 y? – y³, (a) Sketch the direction field and the solutions curves for y(0) to solve the DE! Drawing solutions for the given ICs should be enough to give you the qualitative behaviour of the direction field and solutions. (You are not allowed to use any graphical software). -3, 1, 3. You do not have (b) Based on the direction field (a), determine how the behaviour of the solutions y for large x (i.e., as x → +) depends on different initial values of y at x = 0.

3. Consider the DE 4 = 2 y? – y³, (a) Sketch the direction field and the solutions curves for y(0) to solve the DE! Drawing solutions for the given ICs should be enough to give you the qualitative behaviour of the direction field and solutions. (You are not allowed to use any graphical software). -3, 1, 3. You do not have (b) Based on the direction field (a), determine how the behaviour of the solutions y for large x (i.e., as x → +) depends on different initial values of y at x = 0.

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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3. Consider the DE 4 = 2 y? – y³, (a) Sketch the direction field and the solutions curves for y(0) to solve the DE! Drawing solutions for the given ICs should be enough to give you the qualitative behaviour of the direction field and solutions. (You are not allowed to use any graphical software). -3, 1, 3. You do not have (b) Based on the direction field (a), determine how the behaviour of the solutions y for large x (i.e., as x → +0) depends on different initial values of y at x = 0.
Transcribed Image Text:3. Consider the DE 4 = 2 y? – y³, (a) Sketch the direction field and the solutions curves for y(0) to solve the DE! Drawing solutions for the given ICs should be enough to give you the qualitative behaviour of the direction field and solutions. (You are not allowed to use any graphical software). -3, 1, 3. You do not have (b) Based on the direction field (a), determine how the behaviour of the solutions y for large x (i.e., as x → +0) depends on different initial values of y at x = 0.
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