December 1st, 2018, 11:23 AM  #1 
Member Joined: Oct 2012 Posts: 76 Thanks: 0  Prove that
If xy^2=(x+y)^3 prove that: x^2y''xy'+y=0 
December 1st, 2018, 03:26 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,622 Thanks: 2075 
If y/x is real, solving xy² = (x + y)³ gives y = cx, where c is a constant (equal to approximately 0.43). It's easy to show that y = cx, where c is a constant, is a solution of x²y''  xy' + y = 0. 

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