1550078481-Ordinary_Differential_Equations__Roberts_

380 Ordinary Differential Equations

6. Consider the homogeneous linear system

(24)

a. Verify that

are linearly independent solutions on (0, oo) of (24).

b. Write the general solution of (24).

c. Verify that

Yp = (-~) x

2

is a particular solution of the nonhomogeneous linear system

(25)

d. Write the general solution of (25).

I n exercises 7-1 6 find the real general solut ion of the homogeneou s

linear system y' = Ay for the given matrix A.

G

1

-2)

(-!

• 5

7. 3 -2 8. 4 -;)
   1 -3 - 5 -3

u

6

J) (-l

2

9. 3 10. 4 -3-2 )
   -4 0 1