Question

find the general solution of the following differential equation: dy/dx + y/x = y^3

Answer 1

find your \[\mu\]

Answer 2

integrate 1/x

Answer 3

e is going to be raised by this

Answer 4

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

Answer 5

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

Answer 6

e^\[\int\limits_{}\] 1/x

Answer 7

e^lnx= just x

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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.

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

sorry for the confusion.

Answer 23

its ok thank you for trying.. its much appreciated

Answer 24

this thing is not linear

Answer 25

can you help me?

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

i just need a solution, thats all.

Answer 31

If you want the solution, you can use wolframalpha

y^2=-1/(-Cx^2-2x)

Answer 32

thanks i guess