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Consider the Initial Value Problem (IVT) dy = Axy, y(0) = 1, da where A is a positive constant. The Euler's Method for the IVT using the step size Ax = 1 gives y The Euler's Method for the IVT using the step size Ax = 0.5 gives y x = 1. We expect to obtain a better approximation when using Ax = [Select] [Select] [Select] V when x = 1 when

Consider the Initial Value Problem (IVT) dy = Axy, y(0) = 1, da where A is a positive constant. The Euler's Method for the IVT using the step size Ax = 1 gives y The Euler's Method for the IVT using the step size Ax = 0.5 gives y x = 1. We expect to obtain a better approximation when using Ax = [Select] [Select] [Select] V when x = 1 when

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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The first one I tried using the linear approximation, but my answer was really messy and complex. The second one I generated the slope field, but cannot find the second equilibrium. I do think that when it equals 2, it's stable. Please explain and answer it, thank you!

Consider the Initial Value Problem (IVT) dy = Axy, y(0) = 1, dx where A is a positive constant. The Euler's Method for the IVT using the step size Ax = 1 gives y The Euler's Method for the IVT using the step size Ax = 0.5 gives y x = 1. We expect to obtain a better approximation when using Ax = [Select] [Select] [Select] when x = 1 ✓ when
Transcribed Image Text:Consider the Initial Value Problem (IVT) dy = Axy, y(0) = 1, dx where A is a positive constant. The Euler's Method for the IVT using the step size Ax = 1 gives y The Euler's Method for the IVT using the step size Ax = 0.5 gives y x = 1. We expect to obtain a better approximation when using Ax = [Select] [Select] [Select] when x = 1 ✓ when
For the differential equation - (1+y)(1y) there are 2 equilibrium solutions. dx The first equilibrium solution is 2 which is stable The second equilibrium solution is 0 which is unstable
Transcribed Image Text:For the differential equation - (1+y)(1y) there are 2 equilibrium solutions. dx The first equilibrium solution is 2 which is stable The second equilibrium solution is 0 which is unstable
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