Question

Please help. Differential Eq. finding the particular solution of a nonhomogeneous differentail eq. given:
(D^2-3D+2)y=sin(e^(-x)).

Answer 1

did you find the homogeneous soln. already?

Answer 2

yes.

Answer 3

the roots are 2 and 1

Answer 4

whats D ?

Answer 5

differential operator

Answer 6

it may be above my standard then,,hmm..

Answer 7

you sure it's sin(e^-x)?
non elementary integral...

Answer 8

yes.

Answer 9

The answer in the book should be yp= =e^2xsine^-x, but i always get e^2xsine^-x +2sine^-x

Answer 10

its -e^2xsine^-x .sorry typo

Answer 11

-e^x cos(e^(-x)) is a good trial function...

Answer 12

oh..

Answer 13

-e^2xsine^-x is the forcing function?

Answer 14

the particular solution.

Answer 15

ah ok... e^2xsine^-x +2sine^-x is what your getting using what as a trial function?

Answer 16

Asine^-x

Answer 17

try that with an e^-x out front...

Answer 18

the problem is, that if you just use a trial soln. like sin(e^-x) all your terms will contain e^-x...
but if you use a trial like e^xsin(e^-x) then you'll get term that are just sinusoids... because when the chain rule is applied to e^x sin(e^-x) you get a term with e^x*e^-x (1)

Answer 19

see what I mean?

Answer 20

umm..i'll try thanks

Answer 21

are you supposed to be using some more explicit method than just choosing a trial solution?