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Suppose you have a differential equation of the form x'(t) = Ax(t) with A a 2x2 matrix. Match the information about the eigenvalues A1, A2 of A with properties of solutions x(t). Assume that vi is an eigenvector of A with eigenvalue Ai, for i = 1, 2. A1, A2 are real and distinct As As are purely imaginary, i.e. have the form tib for some positive real number b. A1, A2 are imaginary but not purely imaginary, i.e. have the form a ±ib for a nonzero real number a and a positive real number b. Drop blocks here Solution curves are always straight lines. Solution curves are ellipses centered at the origin. Solution curves are spirals. Drag blocks from here The general solution of the system is x(t)=evie+cavatar

Suppose you have a differential equation of the form x'(t) = Ax(t) with A a 2x2 matrix. Match the information about the eigenvalues A1, A2 of A with properties of solutions x(t). Assume that vi is an eigenvector of A with eigenvalue Ai, for i = 1, 2. A1, A2 are real and distinct As As are purely imaginary, i.e. have the form tib for some positive real number b. A1, A2 are imaginary but not purely imaginary, i.e. have the form a ±ib for a nonzero real number a and a positive real number b. Drop blocks here Solution curves are always straight lines. Solution curves are ellipses centered at the origin. Solution curves are spirals. Drag blocks from here The general solution of the system is x(t)=evie+cavatar

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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Suppose you have a differential equation of the form x'(t) = Ax(t) with A a 2x2 matrix. Match the information about the eigenvalues A1, A2 of A with properties of solutions x(t). Assume that vi is an eigenvector of A with eigenvalue Ai, for i = 1, 2. A1, A2 are real and distinct As As are purely imaginary, i.e. have the form tib for some positive real number b. A1, A2 are imaginary but not purely imaginary, i.e. have the form a ±ib for a nonzero real number a and a positive real number b. Drop blocks here Solution curves are always straight lines. Solution curves are ellipses centered at the origin. Solution curves are spirals. Drag blocks from here The general solution of the system is x(t)=evie+cavatar
Transcribed Image Text:Suppose you have a differential equation of the form x'(t) = Ax(t) with A a 2x2 matrix. Match the information about the eigenvalues A1, A2 of A with properties of solutions x(t). Assume that vi is an eigenvector of A with eigenvalue Ai, for i = 1, 2. A1, A2 are real and distinct As As are purely imaginary, i.e. have the form tib for some positive real number b. A1, A2 are imaginary but not purely imaginary, i.e. have the form a ±ib for a nonzero real number a and a positive real number b. Drop blocks here Solution curves are always straight lines. Solution curves are ellipses centered at the origin. Solution curves are spirals. Drag blocks from here The general solution of the system is x(t)=evie+cavatar
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