The solution of the differential equation `{1/x-y^(2)/(x-y)^(2)}dx+{x^(2)/(x-y)^(2)-1/y}dx=0` isA. ` In |x/y|+(xy)/((x-y))=C`B. ` In |xy|+(xy)/((x-y))=C`C. ` (xy)/((x-y))=Ce^(x//y)`D. ` (xy)/((x-y))=Ce^(xy)`

The solution of the differential equation `{1/x-y^(2)/(x-y)^(2)}dx+{x^

1.	The solution of the differential equation `{1/x-y^(2)/(x-y)^(2)}dx+{x^(2)/(x-y)^(2)-1/y}dx=0` isA. ` In \|x/y\|+(xy)/((x-y))=C`B. ` In \|xy\|+(xy)/((x-y))=C`C. ` (xy)/((x-y))=Ce^(x//y)`D. ` (xy)/((x-y))=Ce^(xy)`
Answer» Correct Answer - a The given equation can be written as ` ((dx)/y-(dy)/y )+(x^(2)dy-y^(2)dx)/((x-y)^(2))=0` ` rArr ((dx)/x - (dy)/y)+(((dy)/(y^(2)) -(dx)/(x^(2))))/ ((1/y-1/x)^(2))=0` ` rArr ((dx)/x - (dy)/y)+(((dy)/(y^(2)) -(dx)/(x^(2))))/ ((1/x-1/y)^(2))=0` On integrating both sides , we get ` In \|x\| - In \|y\| - 1/((1/x-1/y))=C` ` rArr In \|x/y\| = (xy)/((y-x))= C rArr In \|x/y\| +(xy)/((x-y)) = C`

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The solution of the differential equation `{1/x-y^(2)/(x-y)^(2)}dx+{x^(2)/(x-y)^(2)-1/y}dx=0` isA. ` In |x/y|+(xy)/((x-y))=C`B. ` In |xy|+(xy)/((x-y))=C`C. ` (xy)/((x-y))=Ce^(x//y)`D. ` (xy)/((x-y))=Ce^(xy)`

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