Up: 10.47 Previous: 10.47, §1 Asked

10.47, §2 Solution

y'' - 2 y' + y = 3 ex

Homogeneous equation:

yh = C1 ex + C2 x ex

Particular solution:

yp'' - 2 yp' + yp = 3 ex

Particular solutions yp = ex or yp = x ex don't work. Try

yp'' - 2 yp' + yp = C ex 2

so C=1.5.

Total solution:

y = 1.5 x2 ex + C1 ex + C2 x ex


Up: 10.47 Previous: 10.47, §1 Asked