solve the following system for A and B AexBe2x3 Aex2Be2x5Sol

solve the following system for A and B. Ae^-x+Be^2x=3 -Ae^-x+2Be^2x=-5

lets say

e^(-x) = p

e(2x) = q

Ap + Bq = 3...............(1)

-Ap + 2Bq = -5..........(2)

adding (1) and (2)

3 Bq = -2

Bq = -2/3

B = -2/3q

B = -2/(3e^(2x))

taking Bq = -2 in eq(1)

Ap = 3 - Bq

Ap = 3 - (-2/3)

Ap = 11/3

A = 11/3p

A = 11 /3 e(-x)

A = 11 e^x /3