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have you tried Bernoulli's?

dx/dt = x+x^3
divide by x+x^3
multiply by dt

the final answer should be
\[x=\pm \sqrt{C ^{2t}/(1-Ce ^{2t})}\]

Multiplying by dt is impossible! Rates of change are as is.

lol

you get
\[\frac{ 1 }{ x+x^3 }dx=dt\]

but how do you integrate this??

oh that wasn't your answer?

book's answer?

no now You have to integrate both sides.. i am trying to get x by itself

but how do you do partial fraction decomposition?

use partial frac. expansion on 1/(x+x^3)

A / x + Bx /(x^2+1)

thats where i messed up... i didnt put an x after the B

Algebraic, YES, nice going!

_Multiplying by dt is impossible! Rates of change are as is._

go learn the chain rule