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Differential equation of dy/dx = (2x-y+4)/ (4x-2y +1)

  1. Feb 17, 2016 #1
    1. The problem statement, all variables and given/known data
    I'm asked to use the transformation of v= 2x-y to solve dy/dx = (2x-y+4)/ (4x-2y +1)


    the answer given is (2/9)(6x-3y-2) +(7/9)ln(6x-3y-2) = x +c , i got (2/9)(6x-3y) +(7/9)ln(6x-3y-2) = x +c , what's wrong with my working ?

    2. Relevant equations


    3. The attempt at a solution
     

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  3. Feb 17, 2016 #2

    mfb

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    Staff: Mentor

    The two answers differ by a constant summand of 4/9. As you have "+c" anyway, this difference does not matter.
     
  4. Feb 18, 2016 #3
    lol , why the author wanna dd in another (2/9)(-2) into the answer ? this is confusing ...
     
  5. Feb 18, 2016 #4

    HallsofIvy

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    Presumably, because the author used a different method to arrive at a solution. In any case, the point is that, because the derivative of a constant is 0, two functions, differing by a constant, can be solutions to the same first order differential equation.
     
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