## anonymous 3 years ago how to solve this diff equation?? dx/dt−x^3=x

1. anonymous

have you tried Bernoulli's?

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. anonymous

lol

6. anonymous

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

7. anonymous

but how do you integrate this??

8. 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

9. anonymous

@haganmc ... looks good to me.

10. anonymous

11. anonymous

12. anonymous

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

13. anonymous

but how do you do partial fraction decomposition?

14. anonymous

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

15. anonymous

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

16. anonymous

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

17. anonymous

Algebraic, YES, nice going!

18. anonymous

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

19. anonymous

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

20. anonymous

go learn the chain rule

21. 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.