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Dif. equation

  1. Jan 19, 2009 #1
    hey, i have some problems with this diff. equation
    dy/dx=(2x+y-3)^(1/2)
    i tried to do some substitution
    v=2x+y-3
    then
    dv/dx=2+dy/dx
    dy/dx=dv/dx-2
    then i substituted back into original equation
    dv/dx-2=v^(1/2)
    dv/(v^(1/2)+2)=dx
    integrated and got something like this
    2v^(1/2)-4ln(v^(1/2)+2)=x+c

    i do not know whether this is the correct method and what to do with 2v^(1/2)-4ln(v^(1/2)+2)=x+c

    thanks for the advice
     
  2. jcsd
  3. Jan 19, 2009 #2

    Dick

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    Science Advisor
    Homework Helper

    Your solution looks just fine. About all you can do is put v=2x+y-3 back in. Sometimes you get solutions where you can't solve for y as a function of x in a closed form.
     
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