Phase Portraits for Linear System of DEs - Assignment | MATH 3107, Assignments of Differential Equations

Download Phase Portraits for Linear System of DEs - Assignment | MATH 3107 and more Assignments Differential Equations in PDF only on Docsity! Phase Portraits for Linear Systems of DE’s Math 3107 Differential Equations Dr. Howard These problems will not be collected; they are for your practice. For each system of differential equations: ⋅ find the eigenvalues and eigenvectors of the associated matrix, ⋅ sketch lines in the direction of each eigenvector (unless complex), and ⋅ sketch the associated phase portrait, showing representative solution curves with their orientation. 1. dx dt = −1x + 7y, dy dt = −3y 2. dx dt = 3x + 2y, dy dt = 2y 3. dx dt = x + 3y, dy dt = 3x + y 4. dx dt = 23x − 18y, dy dt = 32x − 25y 5. dx dt = 7x + 10y, dy dt = −4x − 5y 6. dx dt = 7x + 15y, dy dt = −6x − 11y 7. dx dt = 6x + 10y, dy dt = −4x − 6y 1