how to solve this diff equation?? dx/dt−x^3=x

Question

lgbasallote · Answer

have you tried Bernoulli's?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

lol

anonymous · Answer

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

anonymous · Answer

but how do you integrate this??

anonymous · Answer

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 · Answer

@haganmc ... looks good to me.

anonymous · Answer

oh  that wasn't your answer?

anonymous · Answer

book's answer?

anonymous · Answer

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

anonymous · Answer

but how do you do partial fraction decomposition?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Algebraic, YES, nice going!

anonymous · Answer

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

anonymous · Answer

That is correct.  What you are actually doing is separation of variables,  It is an important distinction!!!

anonymous · Answer

go learn the chain rule

anonymous · Answer

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.