Question

Find the particular solution for y''-4y'-5y= -6xe^-x

Answer 1

r^2-4r-5
(r-5)(r+1)

Ce^-t + C e^5t

so no worry about linearity

Answer 2

Can you show the process?

Answer 3

sorry we do have to worry about linearity since your input function -6xe^-x has e^-x

Answer 4

so we try (Ax^2+Bx+C)e^-x

Answer 5

put it into your function

Answer 6

I dont get it

Answer 7

you don't get what?

Answer 8

How to solve this

Answer 9

we haven't solved it yet

Answer 10

((Ax^2+Bx+C)e^-x)'' - 4((Ax^2+Bx+C)e^-x)' -5((Ax^2+Bx+C)e^-x)

Answer 11

and you have to solve for A , B and C

Answer 12

ok

Answer 13

when I simplify it , I get
\[2 e^{-x} (A-3 B-6 A x)\]

Answer 14

we set it equal to your input equation
-6xe^-x

Answer 15

-12 A=-6

A=1/2

Answer 16

2A-6B=0
1-6B=0
B=1/6

Answer 17

A x^2 + B x ) e^-x

1/2 x^2 +1/6 x) e^-x