Question

Find the part of the complementary function x^(2)y" - x(x + 2)y' + (x + 2)y =(x^3)(e^x)

Answer 1

Auxillary equation of above differential equation is (D

2

+1)y=0.

⇒

dx

2

d

2

y

+y=0

⇒y=Acosx+Bsinx