Page 125 - Schaum's Outline of Differential Equations

108 VARIATION OF PARAMETERS [CHAP. 12

We assume, therefore, that

Equations (12.6), with N replacing y, become

The solution of this set of equations is

and

Thus,

and (1) becomes

The general solution is

12.7. Solve

Here n = 1 and (from Chapter 6) hence,

9
4
4
Since yi=x 4 and (f>(x) = x , Eq. (12.7) becomes v[x^ = x , from which we obtain v{ = x s and Vi=x /9.
s
Equation (1) now becomes V D = x /9, and the general solution is therefore
(Compare with Problem 6.6.)

(4)
12.8. Solve y = 5.x by variation of parameters.
2
3
Here n = 4 and y h = Cj + c 2x + c^x + c^x ; hence,

2
3
Since y± = l,y 2 = x, y 3 = x ,y 4 = x , and <j>(x) = 5x, it follows from Eq. (12.4), with n = 4, that