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

  1. Feb 14, 2016 #1
    1. The problem statement, all variables and given/known data
    i am given dy/dx +( y/x ) = x(y^3) , using transformation of function = y=v/x , but my ans is wrong , which part of my working is wrong ?

    2. Relevant equations


    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Feb 14, 2016 #2

    SammyS

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    It's very difficult to read your images.

    Can you type them out?
     
  4. Feb 14, 2016 #3
    Which part of the working that you can't read?
     
  5. Feb 14, 2016 #4

    SammyS

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    None of it is easy to read.

    I did zoom in & struggled through.

    When you substitute back in for v (to eliminate v) what did you plug in ?


    From now on, please try to follow the forum rules more closely.
     
  6. Feb 15, 2016 #5
    ok , thanks for pointing out my mistake
     
  7. Feb 15, 2016 #6
    This is actually a really cool problem, it's a "Reverse" homogeneous equation.
     
  8. May 13, 2016 #7
    There is another method to solve this Differential equation is by converting it to exact form

    multiply the whole equation by xdx

    => ## xdy + ydx = x^2y^3dx ##
    now multiply and divide by x on RHS

    ## xdy + ydx = (xy)^3(dx/x) ##

    now using xdy + ydx = d(xy)

    ## \frac {d(xy)} {(xy)^3} = \frac {dx} {x} ##

    ## \int \frac {d(xy)} {(xy)^3} = \int \frac {dx} {x} ##

    now it is easily integrable
     
    Last edited: May 13, 2016
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