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Basic Diffy Q

  1. Sep 15, 2012 #1
    1. The problem statement, all variables and given/known data
    [itex]dy/dx = 1/(x+y)[/itex]


    2. Relevant equations
    Errr. None that I know of.


    3. The attempt at a solution
    [itex]
    v=x+y
    [/itex]

    [itex]
    dy/dx=1/v
    [/itex]

    [itex]
    dv/dx=1+dy/dx
    [/itex]

    [itex]
    dv/dx=1+1/v
    [/itex]

    [itex]
    dv/dx=(v+1)/v
    [/itex]

    [itex]
    dv*v/(v+1)=dx
    [/itex]

    [itex]
    v+1/(v+1) - 1/(v+1) = v/(v+1)
    [/itex]

    [itex]
    \int 1\,dv - \int 1/(v+1)\,dv=\int 1\,dx
    [/itex]

    [itex]
    v - \log (v+1) = x + C
    [/itex]

    [itex]
    e^v/(v+1)=Ce^x
    [/itex]

    [itex]
    e^(x+y)/(x+y+1)=Ce^x
    [/itex]


    I'm just wondering whether I can simplify this or maybe solve it another way so I can get y= (stuff)
     
  2. jcsd
  3. Sep 15, 2012 #2

    Mark44

    Staff: Mentor

    Assuming your work is correct (I didn't check it), you can leave the solution in implicit form. You might not be able to solve the equation you ended up with for y as an explicit function of x.
     
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