SOLUTION: Solve the following differential equation: (1−(2/y)+x)(dy/dx)+y=(2/x)−1. My answer is x+y+xy-2ln(xy)=constant. but is wrong.

Algebra ->  Equations -> SOLUTION: Solve the following differential equation: (1−(2/y)+x)(dy/dx)+y=(2/x)−1. My answer is x+y+xy-2ln(xy)=constant. but is wrong.      Log On


   

Question 1184043: Solve the following differential equation:
(1−(2/y)+x)(dy/dx)+y=(2/x)−1.
My answer is x+y+xy-2ln(xy)=constant. but is wrong.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
You said your answer was
+x+%2B+y+%2B+xy+-+2ln%28xy%29+=+c, for constant c.
If you apply implicit differentiation on this equation, you will get



<===> 1+%2B+dy%2Fdx+%2B+y+%2B+x%2A%28dy%2Fdx%29+-+2%2Fx+-+%282%2Fy%29%2A%28dy%2Fdx%29++=+0
<===> 1+%2B+%281%2Bx+-+2%2Fy%29%28dy%2Fdx%29+%2B+y+-+2%2Fx++=+0
<===> %281%2Bx+-+2%2Fy%29%28dy%2Fdx%29+%2B+y+++=+2%2Fx+-+1, which is exactly the given D.E.

Better ask your instructor as to what particular detail you messed up at.