Consider the ODE y' = y(1 – 4) • What is the order of the D.E.? Is it a linear or a non linear D.E.? • What else can you tell about this D.E. by looking at the RHS? • A direction field is shown below: Find all equilibrium solutions and sketch the solution that satisfies y(0) = 1 • By looking at the direction field, what can you tell about the behavior of the solution for the IVP with initial condition y(1)=-3? • Compare your conclusion from above with the solution for IVP with initial condition y(1)=3
Consider the ODE y' = y(1 – 4) • What is the order of the D.E.? Is it a linear or a non linear D.E.? • What else can you tell about this D.E. by looking at the RHS? • A direction field is shown below: Find all equilibrium solutions and sketch the solution that satisfies y(0) = 1 • By looking at the direction field, what can you tell about the behavior of the solution for the IVP with initial condition y(1)=-3? • Compare your conclusion from above with the solution for IVP with initial condition y(1)=3
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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Transcribed Image Text:Consider the ODE y' = y(1 – 4)
• What is the order of the D.E.? Is it a linear or a non linear D.E.?
• What else can you tell about this D.E. by looking at the RHS?
• A direction field is shown below: Find all equilibrium solutions and sketch the solution that
satisfies y(0) = 1
• By looking at the direction field, what can you tell about the behavior of the solution for the IVP
with initial condition y(1)=-3?
• Compare your conclusion from above with the solution for IVP with initial condition y(1)=3
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