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Math Help - Differential eqn

  1. #1
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    Differential eqn

    find the general solution of Differential eqn-codecogseqn-13-.gif

    i know this is a first order non linear differential eqn

    but how to solve this equation

    i divided by xy tried to make this exact and then find the integrating factor but i am unable to do so

    help
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  2. #2
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    Re: Differential eqn

    Quote Originally Posted by prasum View Post
    find the general solution of Click image for larger version. 

Name:	CodeCogsEqn (13).gif 
Views:	17 
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ID:	26657
    i know this is a first order non linear differential eqn
    but how to solve this equation
    i divided by xy tried to make this exact and then find the integrating factor but i am unable to do so
    help
    I suppose that it is a textbook exercice. So, it cannot be as difficult as the solving of the above ODE.
    This draw to think that there is a typo in the equation.
    For example, the corrected ODE might be as shown below. Then the integrating factor would be 1/(xy)^4
    Attached Thumbnails Attached Thumbnails Differential eqn-corrected-ode.jpg  
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  3. #3
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    Re: Differential eqn

    There is no typo in the problem
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    Re: Differential eqn

    Quote Originally Posted by prasum View Post
    find the general solution of Click image for larger version. 

Name:	CodeCogsEqn (13).gif 
Views:	17 
Size:	1.2 KB 
ID:	26657

    i know this is a first order non linear differential eqn

    but how to solve this equation

    i divided by xy tried to make this exact and then find the integrating factor but i am unable to do so

    help
    It isn't exact, I can't find an integrating factor, and it's not homogeneous. I'm starting to side with "JJ". You may have transcribed it correctly, but I'm guessing the book itself might have a typo.

    -Dan
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  5. #5
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    Re: Differential eqn

    i divided it by xy then separated dx and dy terms to get
    ydx+xdy+2xy^3dx-x^2ydy=0
    then
    d(xy)+i can make this part exact by calculating the integrating factor in terms of y and then solving it
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  6. #6
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    Re: Differential eqn

    Quote Originally Posted by prasum View Post
    i divided it by xy then separated dx and dy terms to get
    ydx+xdy+2xy^3dx-x^2ydy=0
    then
    d(xy)+i can make this part exact by calculating the integrating factor in terms of y and then solving it
    Take into consideration the answers already given and conclude by yourself.
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