Question

Non-Homogeneous equation,i needed help figuring the particular solution to a problem or how to make the guess for it

Answer 1

y′′ − 3y′ + 2y  =  4x + e^(2x)

Answer 2

i figured out the complimentary part just need help with particular solution because im coming up empty handed

Answer 3

in case you are wonderin i made the guess Ax+B+C*e^(2x)
also hi Zarkon =)

Answer 4

what is the solution to \[x^2-3x+2=0\]

Answer 5

(x-2)(x-1)=0
x=2
x=1
y=c1*e^(2x)+c2*e^(x)

Answer 6

so x=2 is a solution...that should help you with you guess

Answer 7

for particular solution? sorry im just learning this but i dont see how

Answer 8

yes

Answer 9

can you explain how i should use my complimenary solution root to guess particular solution

Answer 10

since it is this form 4x + e^(2x) i thought the guess should be in the form Ax+B+C*e^(2x)

Answer 11

Ax+B+C*x*e^(2x)

Answer 12

what prompted u to guess the extra x?

Answer 13

you multiply by x since 2 is a solution to the auxiliary equation

Answer 14

so if there is more than one root to the auxilary equation? or just 2 in particular

Answer 15

the 2


since on the RHS of the eaution we have \(e^{2x}\) ... a 2 in the exponent

Answer 16

equation

Answer 17

OH
My god thankyou thats actually something never explained

Answer 18

so if your root exists in the exponential equation you should multiply by x to make it equivalent

Answer 19

if the 2 had been a repeated root then you would have multiplied bt \(x^2\) and not just \(x\)

Answer 20

yes that makes so much more sense also one last question
if there was (x-2)(x-3) but the exponent to was to the power e^(4x) we wouldnt multiply by x right?

Answer 21

what book do you use

Answer 22

correct

Answer 23

for engineers book one sec lemme google it

Answer 24

http://www.amazon.ca/Calculus-Scientists-Engineers-Early-Transcendentals/dp/0321785371

Answer 25

but i think a newer version but i cant find it lol

Answer 26

http://mcs258.cankaya.edu.tr/uploads/files/Fundamental%20of%20Diff.%20Eqn.(8.Edition).pdf

Answer 27

may your drule empire be everlasting king zarkon

Answer 28

look at the book page 186

Answer 29

its loading..............

Answer 30

ah

Answer 31

should i post another question in another place or is it ok if i post here

Answer 32

its a different approach to the standard homogeneous equations so it kinda threw me off

Answer 33

I have to go away...so make a new post

Answer 34

KK THANKS AGAIN LORD ZARKON

Answer 35

np