Assignment 8 (with solutions)

due Friday, Mar. 22

3.5.26 Solution

3.7.30 Solution

7.1.10 Solution

7.1.22 Solution

7.2.23 Solution

7.5.16 Solution

E.1      Solve using eigenvalues and eigenvectors:

(a)      $$\bold x' = \pmatrix{3 & 4\cr 5 & -5\cr} \bold x$$

Solution

(b)      $$\bold x' = \pmatrix{3 & -1\cr 1 & 1\cr} \bold x$$

Solution

E.2      Solve by reducing to a second order linear equation:

(a)      $$\bold x' = \pmatrix{3 & 4\cr 5 & -5\cr} \bold x + {\rm e}^{-2t} \pmatrix{2\cr 1\cr}$$

Solution

(b)      $$\bold x' = \pmatrix{3 & -1\cr 1 & 1\cr} \bold x + \pmatrix{\cos(t)\cr \sin(t)\cr}$$

Solution