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lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
have you tried Bernoulli's?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
dx/dt = x+x^3 divide by x+x^3 multiply by dt
 2 years ago

haganmc Group TitleBest ResponseYou've already chosen the best response.0
the final answer should be \[x=\pm \sqrt{C ^{2t}/(1Ce ^{2t})}\]
 2 years ago

ironmanjimbo Group TitleBest ResponseYou've already chosen the best response.0
Multiplying by dt is impossible! Rates of change are as is.
 2 years ago

haganmc Group TitleBest ResponseYou've already chosen the best response.0
you get \[\frac{ 1 }{ x+x^3 }dx=dt\]
 2 years ago

haganmc Group TitleBest ResponseYou've already chosen the best response.0
but how do you integrate this??
 2 years ago

ironmanjimbo Group TitleBest ResponseYou've already chosen the best response.0
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
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
@haganmc ... looks good to me.
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
oh that wasn't your answer?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
book's answer?
 2 years ago

haganmc Group TitleBest ResponseYou've already chosen the best response.0
no now You have to integrate both sides.. i am trying to get x by itself
 2 years ago

haganmc Group TitleBest ResponseYou've already chosen the best response.0
but how do you do partial fraction decomposition?
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
use partial frac. expansion on 1/(x+x^3)
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
A / x + Bx /(x^2+1)
 2 years ago

haganmc Group TitleBest ResponseYou've already chosen the best response.0
thats where i messed up... i didnt put an x after the B
 2 years ago

ironmanjimbo Group TitleBest ResponseYou've already chosen the best response.0
Algebraic, YES, nice going!
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
_Multiplying by dt is impossible! Rates of change are as is._
 2 years ago

ironmanjimbo Group TitleBest ResponseYou've already chosen the best response.0
That is correct. What you are actually doing is separation of variables, It is an important distinction!!!
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.1
go learn the chain rule
 2 years ago

ironmanjimbo Group TitleBest ResponseYou've already chosen the best response.0
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.
 2 years ago
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