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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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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