integrating factor by inspection:
(2x2+y)dx+(x2y−x)dy=0
Solution:
(2x2dx+x2ydy)+(ydx−xdy)=0,
x2x2(2dx+ydy)−x2(xdy−ydx)=0 ,
(2dx+ydy)−x2(xdy−ydx)=0 ,
d(2x+2y2)−d(xy)=0 ,
d(2x+2y2−xy)=0 ,
2x+2y2−xy=C ,
Answer: U(x,y)=2x+2y2−xy=C , integrating factor is μ(x)=x21
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