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anonymous

  • 5 years ago

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

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  1. anonymous
    • 5 years ago
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    find your \[\mu\]

  2. anonymous
    • 5 years ago
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    integrate 1/x

  3. anonymous
    • 5 years ago
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    e is going to be raised by this

  4. anonymous
    • 5 years ago
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    can you please solve it step by step because im really bad at math

  5. anonymous
    • 5 years ago
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    in the end you are just going to end up with x, so multiply both sides of the equation by this

  6. anonymous
    • 5 years ago
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    e^\[\int\limits_{}\] 1/x

  7. anonymous
    • 5 years ago
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    e^lnx= just x

  8. anonymous
    • 5 years ago
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    x(dy/dx)+y=y^3x

  9. anonymous
    • 5 years ago
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    x(dy/dx)+y is just (xy)(dy/dx)

  10. anonymous
    • 5 years ago
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    from here you can separate and put your y's with dy and x's with dx

  11. anonymous
    • 5 years ago
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    this will give you (dy/y^2)=dx, just integrate now

  12. anonymous
    • 5 years ago
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    god bless you.. but i really suck at math and i have two exams tomorrow so i cant study for them both

  13. anonymous
    • 5 years ago
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    i truly appreciate your help, but if any one of you guys could do the whole thing, you would save my life

  14. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    the final answer should be y=1/-(x+c)

  16. anonymous
    • 5 years ago
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    or play with the constants and you should get y=1/(x+c)

  17. anonymous
    • 5 years ago
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    I don't think that's the solution mathtio, I'm not quite sure what you're doing

  18. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    you are right. I forgot about the exponent in the y.

  21. anonymous
    • 5 years ago
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    attention to detail.....spaceknight should be able to help you better than i can.

  22. anonymous
    • 5 years ago
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    sorry for the confusion.

  23. anonymous
    • 5 years ago
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    its ok thank you for trying.. its much appreciated

  24. anonymous
    • 5 years ago
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    this thing is not linear

  25. anonymous
    • 5 years ago
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    can you help me?

  26. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    @spaceknight, am afraid you cannot get rid of y even if you sub with v.

  29. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    i just need a solution, thats all.

  31. anonymous
    • 5 years ago
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    If you want the solution, you can use wolframalpha y^2=-1/(-Cx^2-2x)

  32. anonymous
    • 5 years ago
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    thanks i guess

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