Question

how would i solve (x double dot) + x(x dot)+x=0

Answer 1

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Answer 2

help

Answer 3

I think you can solve it by reduction of order

Answer 4

how?

Answer 5

you deleted that? it wasnt the same

Answer 6

yea, i had it wrong

Answer 7

that one can be solved differently

Answer 8

i thought reduction of order was for coefficients which are random polynomials of in t

Answer 9

\[x \prime \prime+xx \prime+x=0\]

Answer 10

for this you say let u=dx/dt
than
d^2x/dt^2=u du/dt

Answer 11

than the equation will be
u du/dt + xu+x=0

Answer 12

ahh, that is clever, i will try that

Answer 13

thanks a ton

Answer 14

and I guess you can use an integrating factor to solve this

Answer 15

now I have to go to the shop. If you have a problem just post it

Answer 16

sweet, thanks a ton you are amazing

Answer 17

that integral doesn't make sense, it is with respect to the wrong variable

Answer 18

you have to change u back to x

Answer 19

I did not solve it, what did you get?

Answer 20

ah, i'm saying even setting up the integration factor

Answer 21

dot means that we differentiate with respect to t

Answer 22

x is a function of t, but the integral should be with respect to t

Answer 23

yea, i set up \[u \prime+ux+x=0\]

Answer 24

u du/dt + xu+x=0
du/dt +u/x=-x

Answer 25

u'=u du/dt by the chain rule

Answer 26

e^integral1/x is the integrating factor
that is just x

Answer 27

so multiplying with x gives
xdu/dt+u=-x^2

Answer 28

(xu)dot=-x^2

Answer 29

xu=-(x^3)/3 +C

Answer 30

u=-(x^2)/3 +c/x

Answer 31

u=dx/dt

Answer 32

dx/dt=-(x^2)/3 +c/x

Answer 33

so t= -(x^3)/9 +Clnx

Answer 34

but when you set up that equation du/dt +u/x=-x we should be integrating with respect to t

Answer 35

you are integrating with respect to x

Answer 36

for the integrating factor no

Answer 37

it is only for making it a full derivative

Answer 38

the integrating factor makes sense

Answer 39

I think it is like this, but I would not bet on it :-)

Answer 40

the actual integratioin though does not and why is the equation u du/dt rather than du/dt

Answer 41

u=dx/dt
u dot= x double dot

Answer 42

this part is not 100% clear for me :) but I am sure that is right and comes from the chain rule

Answer 43

I just posted a question about it, maybe some1 is wise

Answer 44

(I'm just a 1st year maths student)

Answer 45

well, thank you for your help, i will check back later. i really appreciate it andras

Answer 46

your welcome