Exercise 4. (Complex Eigenvalues)Consider the system i = x – y, ÿ =x+y a) Write the system in matrix form and find the eigenvalues and eigenvectors (Note: they will be complex valued). b) Write down the general solution for the system of differential equations using only real valued functions. [Hint: use the equality ewt – cos(wt) + i sin(wt)]

Exercise 4. (Complex Eigenvalues)Consider the system i = x – y, ÿ =x+y a) Write the system in matrix form and find the eigenvalues and eigenvectors (Note: they will be complex valued). b) Write down the general solution for the system of differential equations using only real valued functions. [Hint: use the equality ewt – cos(wt) + i sin(wt)]

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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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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Exercise 4.
(Complex Eigenvalues)Consider the system i = x – Y, ÿ = x+Y
a) Write the system in matrix form and find the eigenvalues and eigenvectors (Note: they
will be complex valued).
b) Write down the general solution for the system of differential equations using only real
valued functions. [Hint: use the equality ewt = cos(wt) + i sin(wt)]

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