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3. Linear Systems (a) ii. iii. i. For the following systems, find the general solutions: x' = 10y, y'= -10x; x (0) = 3,y(0) = 4. (Translate into a single second-order equation.) x' = x + 2y, y' = 3x +2y; x(0) = 0, y(0) = -4. (Use eigenvalues.) x = −y, y'=x - 2y. (Use eigenvalues.) L (a) O (O)

3. Linear Systems (a) ii. iii. i. For the following systems, find the general solutions: x' = 10y, y'= -10x; x (0) = 3,y(0) = 4. (Translate into a single second-order equation.) x' = x + 2y, y' = 3x +2y; x(0) = 0, y(0) = -4. (Use eigenvalues.) x = −y, y'=x - 2y. (Use eigenvalues.) L (a) O (O)

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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3. Linear Systems (a) i. ii. iii. iv. For the following systems, find the general solutions: 10y, y' = −10x; x(0) = 3,y(0) = 4. (Translate into a single second-order equation.) x': = x' = x+2y, y' = 3x +2y; x(0) = 0, y(0) = −4. (Use eigenvalues.) x' =y, y'=x - 2y. (Use eigenvalues.) x' = x - 2y, y' = 2x+y; x(0) = 0, y(0) = 4. (Use eigenvalues.) -1 (b) For a non-singular square matrix A, show that A and A have the same eigenvectors. What is the relationship between the eigenvalues?
Transcribed Image Text:3. Linear Systems (a) i. ii. iii. iv. For the following systems, find the general solutions: 10y, y' = −10x; x(0) = 3,y(0) = 4. (Translate into a single second-order equation.) x': = x' = x+2y, y' = 3x +2y; x(0) = 0, y(0) = −4. (Use eigenvalues.) x' =y, y'=x - 2y. (Use eigenvalues.) x' = x - 2y, y' = 2x+y; x(0) = 0, y(0) = 4. (Use eigenvalues.) -1 (b) For a non-singular square matrix A, show that A and A have the same eigenvectors. What is the relationship between the eigenvalues?
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