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Given dr -y? + 2y + 15 (a) Sketch the phase line (portrait) and classify all of the critical (equilibrium) points. Use arrows to indicate flow on the phase line (away or towards a critical point). (b) Next to your phase line, sketch the graph of solutions passing through the given points: y(0) = -4, y(0) = -3, y(0) = 1, y(0) = 6 (c) Find lim y(x) for the solution satisfying the initial condition y(0) = 5. dy (d) State the solution to the initial-value problem = -y² + 2y + 15, y(0) = 5. dr

Given dr -y? + 2y + 15 (a) Sketch the phase line (portrait) and classify all of the critical (equilibrium) points. Use arrows to indicate flow on the phase line (away or towards a critical point). (b) Next to your phase line, sketch the graph of solutions passing through the given points: y(0) = -4, y(0) = -3, y(0) = 1, y(0) = 6 (c) Find lim y(x) for the solution satisfying the initial condition y(0) = 5. dy (d) State the solution to the initial-value problem = -y² + 2y + 15, y(0) = 5. dr

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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My question is in the picture.

I have solved part A and am working on parts B-D. I just cant figure out how to draw y(0) = -3 for part b. I think that the limit as x goes to infinity when y(0)=5 is 5, and I dont know how I should go about part D.

dy 3. Given dx = -y? + 2y + 15 (a) Sketch the phase line (portrait) and classify all of the critical (equilibrium) points. Use arrows to indicated the flow on the phase line (away or towards a critical point). Y= S (b) Next to your phase line, sketch the graph of solutions passing through the given points: y(0) = -4, y(0) = -3, y(0) = 1, y(0) = 6 (c) Find lim y(r) for the solution satisfying the initial condition y(0) = 5. dy = -y? + 2y + 15, y(0) = 5. d.r (d) State the solution to the initial-value problem
Transcribed Image Text:dy 3. Given dx = -y? + 2y + 15 (a) Sketch the phase line (portrait) and classify all of the critical (equilibrium) points. Use arrows to indicated the flow on the phase line (away or towards a critical point). Y= S (b) Next to your phase line, sketch the graph of solutions passing through the given points: y(0) = -4, y(0) = -3, y(0) = 1, y(0) = 6 (c) Find lim y(r) for the solution satisfying the initial condition y(0) = 5. dy = -y? + 2y + 15, y(0) = 5. d.r (d) State the solution to the initial-value problem
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