Question

The following 2 problems you are given x' = Ax + f.
Give the FORM of a particular solution that you get from the technique of undetermined coefficients. You do not need to solve.

Answer 1

a) A = [ 0 1 ] f(t)= [ cos(t) ]
[ -1 0 ] [ sin(2t) ]

Answer 2

I am having trouble understanding what the book says about the different forms for the particular solution.

Answer 3

I think this one would be

xp = Acos(t) + Bsin(t) + Csin(2t) + Dcos(2t)

Answer 4

b) A = [ 0 1 ] f(t)= [ e^(2t) ]
[ 1 0 ] [ e^(-t) ]

Answer 5

I think this one is

xp = Ae^(2t) + Be^(-t)

Answer 6

ex) if f(t) = col(t,e^t,t^2)
xp(t) = At^2 + Bt + c + De^t

Answer 7

Hmm I don't understand this really...
Are you finding eigenvalues and all that kinda stuff? D:
Orrrrr..?

Answer 8

yes, the part I'm studying now is about matrices and eigenvalues. This is part of an initial value problem where we just had to setup the particular solution. I left this 20 pt problem blank on my test :/

Answer 9

Oh my :O

Answer 10

I'm going back through it trying to solve the ones I got wrong, but I don't have the answer, makes it frustrating

Answer 11

@zepdrix this is in an ODE course.

Answer 12

@ChmE I'll have to look back into how to solve this... let me go find my book. :-p

Answer 13

@Hero @phi @jim_thompson5910 Can you check my answers?

Answer 14

thx @oldrin.bataku