Problem 2a)Given the second order equationy"+2ay + (a2 b)y=0,where a and b are real numbers.Find the values of a, b for whichi) all solutions of the equation (Y) tend to zero as t ,ii) all solutions of the equation (Y) are unbounded on the interval (0, o0)b)Show that if y(t) is a solution of the problemy" +ety +y = 0, y(0) = 1, y(0) = 2,%3Dthen(y'(t)² + [y(t)]° < 5, Vt E (0, 00).

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Problem 2 a) Given the second order equation y" + 2ay + (a2 +b)y=0, %3D where a andb are real numbers. Find the values of a, b for which i) all solutions of the equation (Y) tend to zero as t → o, ii) all solutions of the equation (Y) are unbounded on the interval (0, o0) b) Show that if y(t) is a solution of the problem y" +ety +y = 0, y(0) = 1, y(0) = 2, %3D %3D then (y'(t)² + [y(t)]² < 5, VtE (0, 0).

Problem 2 a) Given the second order equation y" + 2ay + (a2 +b)y=0, %3D where a andb are real numbers. Find the values of a, b for which i) all solutions of the equation (Y) tend to zero as t → o, ii) all solutions of the equation (Y) are unbounded on the interval (0, o0) b) Show that if y(t) is a solution of the problem y" +ety +y = 0, y(0) = 1, y(0) = 2, %3D %3D then (y'(t)² + [y(t)]² < 5, VtE (0, 0).

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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Concept explainers

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.

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Problem 2
a)
Given the second order equation
y"+2ay + (a2 b)y=0,
where a and b are real numbers.
Find the values of a, b for which
i) all solutions of the equation (Y) tend to zero as t ,
ii) all solutions of the equation (Y) are unbounded on the interval (0, o0)
b)
Show that if y(t) is a solution of the problem
y" +ety +y = 0, y(0) = 1, y(0) = 2,
%3D
then
(y'(t)² + [y(t)]° < 5, Vt E (0, 00).

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