anonymous
  • anonymous
how would i solve (x double dot) + x(x dot)+x=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Owlfred
  • Owlfred
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anonymous
  • anonymous
help
anonymous
  • anonymous
I think you can solve it by reduction of order

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anonymous
  • anonymous
how?
anonymous
  • anonymous
you deleted that? it wasnt the same
anonymous
  • anonymous
yea, i had it wrong
anonymous
  • anonymous
that one can be solved differently
anonymous
  • anonymous
i thought reduction of order was for coefficients which are random polynomials of in t
anonymous
  • anonymous
\[x \prime \prime+xx \prime+x=0\]
anonymous
  • anonymous
for this you say let u=dx/dt than d^2x/dt^2=u du/dt
anonymous
  • anonymous
than the equation will be u du/dt + xu+x=0
anonymous
  • anonymous
ahh, that is clever, i will try that
anonymous
  • anonymous
thanks a ton
anonymous
  • anonymous
and I guess you can use an integrating factor to solve this
anonymous
  • anonymous
now I have to go to the shop. If you have a problem just post it
anonymous
  • anonymous
sweet, thanks a ton you are amazing
anonymous
  • anonymous
that integral doesn't make sense, it is with respect to the wrong variable
anonymous
  • anonymous
you have to change u back to x
anonymous
  • anonymous
I did not solve it, what did you get?
anonymous
  • anonymous
ah, i'm saying even setting up the integration factor
anonymous
  • anonymous
dot means that we differentiate with respect to t
anonymous
  • anonymous
x is a function of t, but the integral should be with respect to t
anonymous
  • anonymous
yea, i set up \[u \prime+ux+x=0\]
anonymous
  • anonymous
u du/dt + xu+x=0 du/dt +u/x=-x
anonymous
  • anonymous
u'=u du/dt by the chain rule
anonymous
  • anonymous
e^integral1/x is the integrating factor that is just x
anonymous
  • anonymous
so multiplying with x gives xdu/dt+u=-x^2
anonymous
  • anonymous
(xu)dot=-x^2
anonymous
  • anonymous
xu=-(x^3)/3 +C
anonymous
  • anonymous
u=-(x^2)/3 +c/x
anonymous
  • anonymous
u=dx/dt
anonymous
  • anonymous
dx/dt=-(x^2)/3 +c/x
anonymous
  • anonymous
so t= -(x^3)/9 +Clnx
anonymous
  • anonymous
but when you set up that equation du/dt +u/x=-x we should be integrating with respect to t
anonymous
  • anonymous
you are integrating with respect to x
anonymous
  • anonymous
for the integrating factor no
anonymous
  • anonymous
it is only for making it a full derivative
anonymous
  • anonymous
the integrating factor makes sense
anonymous
  • anonymous
I think it is like this, but I would not bet on it :-)
anonymous
  • anonymous
the actual integratioin though does not and why is the equation u du/dt rather than du/dt
anonymous
  • anonymous
u=dx/dt u dot= x double dot
anonymous
  • anonymous
this part is not 100% clear for me :) but I am sure that is right and comes from the chain rule
anonymous
  • anonymous
I just posted a question about it, maybe some1 is wise
anonymous
  • anonymous
(I'm just a 1st year maths student)
anonymous
  • anonymous
well, thank you for your help, i will check back later. i really appreciate it andras
anonymous
  • anonymous
your welcome

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