Question: differential equation solutions

May 03 2013 Ratch 211

     Many times when I use dsolve to find the solution of an equation like x-y/y' = y , I get a term involving the LambertW function.  However, the equation has homogeneous coefficients for dx and dy, so it can easily be solved by substituting y=u*x and separating the variables.  The closed form solution of the above is x+y*ln(y)+c*y = 0 , but I cannot get that answer from Maple.  Is there any way to get Maple to at least attempt a closed form solution?  Thanks, Ratch

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