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10.45, §2 Solution

y'' - 2 y' + y = 3 e2x

Homogeneous equation:

Characteristic polynomial:

has roots :General solution:

yh = C1 ex + C2 x ex

Particular solution:

yp'' - 2 yp' + yp = 3 e2x

Guessing yp = C e2x produces

so C=3 and yp = 3 e2x.

Total solution:

y = 3 e2x + C1 ex + C2 x ex


Up: 10.45 Previous: 10.45, §1 Asked