Systems of ODEs

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The eigenvalues of the coefficient matrix of a linear ODE system determine the system's:

A.Color

B.Stability and behavior over time

C.Size only

D.Number of variables only

A system of linear ODEs $\dot{x} = Ax$ has solutions characterized by the ___ of matrix $A$ .

A.Eigenvalues

B.Determinant only

C.Trace only

D.Rank only

A system of linear first-order ODEs ẋ = Ax is commonly solved using the eigenvalues and eigenvectors of:

A.The vector x

B.The coefficient matrix A

C.The identity matrix

D.The zero matrix

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