36 A- -[% 1)-[* ] -36 in the system x' = Ax; thus A is the negative of the matrix in Example 4. Once again we can solve the system using the principle of time reversal: Replacing t with -t in the right-hand side of the solution in Eq. (19) of Example 4 leads to x(t) = c1 35t + c2 -6
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
Solve the Attachment?
![36
A- -[% 1)-[* ]
-36
in the system x' = Ax; thus A is the negative of the matrix in Example 4. Once again we can
solve the system using the principle of time reversal: Replacing t with -t in the right-hand
side of the solution in Eq. (19) of Example 4 leads to
x(t) = c1
35t + c2
-6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3538d79-dd30-421a-8ca5-873dec048f25%2Fa0c42da5-199f-4630-830b-28b5a88d5f56%2Fzyri1a.png&w=3840&q=75)
What is System of Differential Equation:
A set of finite differential equations is known as a system of differential equations in mathematics. Such a system can be either linear or non-linear. A system of partial differential equations or a system of ordinary differential equations can both be used to describe this one. Eigenvalues and eigenvectors are used to determine the solution.
Given:
Given system is where .
To Determine:
We solve the system.
Given matrix is
In order to determine the solution to the homogeneous system of differential equations , we need to determine the eigenvalues and corresponding eigenvectors of the matrix .
The characteristic polynomial is
Now, solve the characteristic equation . It follows,
Therefore, two eigenvalues are .
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