anonymous
  • anonymous
find the general solution of the following differential equation: dy/dx + y/x = y^3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
find your \[\mu\]
anonymous
  • anonymous
integrate 1/x
anonymous
  • anonymous
e is going to be raised by this

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anonymous
  • anonymous
can you please solve it step by step because im really bad at math
anonymous
  • anonymous
in the end you are just going to end up with x, so multiply both sides of the equation by this
anonymous
  • anonymous
e^\[\int\limits_{}\] 1/x
anonymous
  • anonymous
e^lnx= just x
anonymous
  • anonymous
x(dy/dx)+y=y^3x
anonymous
  • anonymous
x(dy/dx)+y is just (xy)(dy/dx)
anonymous
  • anonymous
from here you can separate and put your y's with dy and x's with dx
anonymous
  • anonymous
this will give you (dy/y^2)=dx, just integrate now
anonymous
  • anonymous
god bless you.. but i really suck at math and i have two exams tomorrow so i cant study for them both
anonymous
  • anonymous
i truly appreciate your help, but if any one of you guys could do the whole thing, you would save my life
anonymous
  • 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.
anonymous
  • anonymous
the final answer should be y=1/-(x+c)
anonymous
  • anonymous
or play with the constants and you should get y=1/(x+c)
anonymous
  • anonymous
I don't think that's the solution mathtio, I'm not quite sure what you're doing
anonymous
  • 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
anonymous
  • 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
anonymous
  • anonymous
you are right. I forgot about the exponent in the y.
anonymous
  • anonymous
attention to detail.....spaceknight should be able to help you better than i can.
anonymous
  • anonymous
sorry for the confusion.
anonymous
  • anonymous
its ok thank you for trying.. its much appreciated
anonymous
  • anonymous
this thing is not linear
anonymous
  • anonymous
can you help me?
anonymous
  • 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
anonymous
  • 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
anonymous
  • anonymous
@spaceknight, am afraid you cannot get rid of y even if you sub with v.
anonymous
  • 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
anonymous
  • anonymous
i just need a solution, thats all.
anonymous
  • anonymous
If you want the solution, you can use wolframalpha y^2=-1/(-Cx^2-2x)
anonymous
  • anonymous
thanks i guess

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