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Which method to use?

  1. Apr 7, 2005 #1
    Hello guys,

    Which method can we use to solve the differential equation below?
    dy/dx= 1/(xy+x^2y^3)

    It doesn't seem to be of any form which I had studied before(linear differential equations,bernoulli,exact differential,homogeneous,seperable equations) for first order differential equations yet it appeared in one of out past examination questions :cry:
  2. jcsd
  3. Apr 7, 2005 #2


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    It's easy.For me

    [tex] \frac{dy}{dx}=\frac{1}{xy+x^{2}y^{3}} [/tex]


    [tex] \frac{dx}{dy}=yx+y^{3}x^{2} [/tex]

    Make the substitution

    [tex] x=\frac{1}{u} [/tex]

    ,under which

    [tex] \frac{dx}{dy}=-\frac{1}{u^{2}}\frac{du}{dy} [/tex]

    Therefore the new ODE is

    [tex] -\frac{1}{u^{2}}\frac{du}{dy}=\frac{y}{u}+y^{3}\frac{1}{u^{2}} [/tex]


    [tex] \frac{du}{dy}=-yu-y^{3} [/tex]

    I trust you can take it from here.It's an nonhomegenous linear ODE...(the homogenous eq is separable).

  4. Apr 7, 2005 #3
    Wow! That was a fast reply. =) Thank you for replying and how do you type the mathematical equations in between? I don't seem to see any functions in this thread which allows us to type mathematical functions?
  5. Apr 7, 2005 #4


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    Write formulas in latex code and use preview option for checking it b4 clicking submit.

  6. Apr 7, 2005 #5
    I see. Thank you for the advice =)
  7. Apr 7, 2005 #6
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