MATH 320: Phase Portraits of Linear Systems with Real Eigenvalues - Prof. Erin K. Mcnelis, Assignments of Differential Equations

Download MATH 320: Phase Portraits of Linear Systems with Real Eigenvalues - Prof. Erin K. Mcnelis and more Assignments Differential Equations in PDF only on Docsity! MATH 320 - Ordinary Differential Equations Section 3.3: Phase Planes for Linear Systems with Real Eigenvalues Friday, April 2, 2004 Saddles dY dt = ( −3 0 0 2 ) Y Eigenvalues: Corresponding Eigenvectors: Origin is a Saddle a=–3, b=c=0, d=2 –4 –2 2 4 y –4 –2 2 4 x Sketch of x(t) and y(t) solutions for x(0) = and y(0) = . More Saddles dY dt = ( 8 −11 6 −9 ) Y Eigenvalues: Corresponding Eigenvectors: Origin is a Saddle a=8, b=–11, c=6, d=–9 –4 –2 2 4 –4 –2 2 4 Sketch of x(t) and y(t) solutions for x(0) = and y(0) = .