## anonymous 5 years ago find the general solution of the following differential equation: dy/dx + y/x = y^3

1. anonymous

find your $\mu$

2. anonymous

integrate 1/x

3. anonymous

e is going to be raised by this

4. anonymous

can you please solve it step by step because im really bad at math

5. anonymous

in the end you are just going to end up with x, so multiply both sides of the equation by this

6. anonymous

e^$\int\limits_{}$ 1/x

7. anonymous

e^lnx= just x

8. anonymous

x(dy/dx)+y=y^3x

9. anonymous

x(dy/dx)+y is just (xy)(dy/dx)

10. anonymous

from here you can separate and put your y's with dy and x's with dx

11. anonymous

this will give you (dy/y^2)=dx, just integrate now

12. anonymous

god bless you.. but i really suck at math and i have two exams tomorrow so i cant study for them both

13. anonymous

i truly appreciate your help, but if any one of you guys could do the whole thing, you would save my life

14. anonymous

This is a bernoulli's equation. You have to make the substitution v=y^(-2). v' will then equal=-2y^(-3)dy/dx. Sub in dy/dx from the original equation. Things will cancel only leaving you with v and x. Solve this new equation as a linear 1st order and then sub back in your v's with y's.

15. anonymous

the final answer should be y=1/-(x+c)

16. anonymous

or play with the constants and you should get y=1/(x+c)

17. anonymous

I don't think that's the solution mathtio, I'm not quite sure what you're doing

18. anonymous

can you please solve the problem step by step because im so tired and i still have so much to study I HONESTLY APPRECIATE YOUR HELP SO MUCH GUYS :) thank you

19. anonymous

mathtio is tryign to solve this as a linear first order, but you can't because the right side is in terms of y and not x

20. anonymous

you are right. I forgot about the exponent in the y.

21. anonymous

attention to detail.....spaceknight should be able to help you better than i can.

22. anonymous

sorry for the confusion.

23. anonymous

its ok thank you for trying.. its much appreciated

24. anonymous

this thing is not linear

25. anonymous

can you help me?

26. anonymous

instead of waiting for every step you can at least try doing it, the problem is pretty straight forward once you get started on it

27. anonymous

yes but my problem is that i dont get it at all.. I have always had problem with math.. i wish i could understand math half as well as you can.. if i knew how to solve it i wouldnt be asking for help :S

28. anonymous

@spaceknight, am afraid you cannot get rid of y even if you sub with v.

29. anonymous

Yes you can. The y's can all be substituted nicely with v's. And, what part of my solution don't you understand? You can't just look at a problem and say you don't get it. If you don't even understand the very basics on how to start, even if I posted step by step solutions you wouldn't get it

30. anonymous

i just need a solution, thats all.

31. anonymous

If you want the solution, you can use wolframalpha y^2=-1/(-Cx^2-2x)

32. anonymous

thanks i guess