Question

how to solve:
(D^2-7D-6)y=e^2x(1+x^2)​

Answer 1

Answer:  144    Explanation:

Aux. eqn is

r3–7r−6=0

with roots −1,−2,3

yc=Ae−x+Be−2x+Ce3x

yp=1(D−3)(D+1)(D+2)e2x(1+x)

=e2x1(D−1)(D+3)(D+4)(1+x)

=e2x1−12+5D+..(1+x)

=e2x1−12(1−5D12)−1(1+x)

=−e2x12(1+5D12+...)(1+x)

=−e2x12(1+x+512+...)

=−e2x(12x+17)144