anonymous
  • anonymous
how to solve this diff equation?? dx/dt−x^3=x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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lgbasallote
  • lgbasallote
have you tried Bernoulli's?
anonymous
  • anonymous
dx/dt = x+x^3 divide by x+x^3 multiply by dt
anonymous
  • anonymous
the final answer should be \[x=\pm \sqrt{C ^{2t}/(1-Ce ^{2t})}\]

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anonymous
  • anonymous
Multiplying by dt is impossible! Rates of change are as is.
anonymous
  • anonymous
lol
anonymous
  • anonymous
you get \[\frac{ 1 }{ x+x^3 }dx=dt\]
anonymous
  • anonymous
but how do you integrate this??
anonymous
  • anonymous
haganmc is right on, what he did is separation of variables which is not the same as multiplying by a component of a rate of change. Well done. Now go with factoring and partial fraction decomposition and you are on your way to a solution
anonymous
  • anonymous
@haganmc ... looks good to me.
anonymous
  • anonymous
oh that wasn't your answer?
anonymous
  • anonymous
book's answer?
anonymous
  • anonymous
no now You have to integrate both sides.. i am trying to get x by itself
anonymous
  • anonymous
but how do you do partial fraction decomposition?
anonymous
  • anonymous
use partial frac. expansion on 1/(x+x^3)
anonymous
  • anonymous
A / x + Bx /(x^2+1)
anonymous
  • anonymous
thats where i messed up... i didnt put an x after the B
anonymous
  • anonymous
Algebraic, YES, nice going!
anonymous
  • anonymous
_Multiplying by dt is impossible! Rates of change are as is._
anonymous
  • anonymous
That is correct. What you are actually doing is separation of variables, It is an important distinction!!!
anonymous
  • anonymous
go learn the chain rule
anonymous
  • anonymous
I don't mind if you do not want to agree with me, but I will simply suggest that you look into what I'm pointing out regarding how the rate of change is separated in such equations. Simply put, it LOOKS like dt was multiplied, but it was not.

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