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Consider the problem y' =1-2.xy, y(0) = 0 . %3D Find the solution of this D.E.

Consider the problem y' =1-2.xy, y(0) = 0 . %3D Find the solution of this D.E.

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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Consider the problem y' =1- 2xy, y(0) = 0 . Find the solution of this D.E. Consider the above problem on R: s. Iy|s1. If f (x, y) =1–2xy, show that f(x, y) < 2, ((x, y) inR and that all the successive 1 aproximations to the solution exist on and their graphs remain in R. Show that f(x, y) satisfies a Lipschitz condition on Rand find the Lipschitz constant. Show that the successive aproximations converge to a solution ø of the initial value problem on
Transcribed Image Text:Consider the problem y' =1- 2xy, y(0) = 0 . Find the solution of this D.E. Consider the above problem on R: s. Iy|s1. If f (x, y) =1–2xy, show that f(x, y) < 2, ((x, y) inR and that all the successive 1 aproximations to the solution exist on and their graphs remain in R. Show that f(x, y) satisfies a Lipschitz condition on Rand find the Lipschitz constant. Show that the successive aproximations converge to a solution ø of the initial value problem on
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