Differential Equations and Linear Algebra, 4th Edition

Section 9.3

1. 1. Linearization at (0, 0): $x\text{′}=200x,y\text{′}=-150y$; phase plane portrait:

   

2. 3. Linearization at (75, 50): $u\text{′}=-300v,v\text{′}=100u$; phase plane portrait:

   

3. 5. The characteristic equation is ${\lambda }^2+45\lambda +126=0$.

4. 7. The characteristic equation is ${(-24-\lambda )}^2-2·{(18)}^2=0$. Phase plane portrait:

   

   Phase plane portrait for the nonlinear system in Problems 4-7:

   

5. 9. The ...