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(x+y(dy)/(dx))/(y-x(dy)/(dx))=(xcos^2(x^...

`(x+y(dy)/(dx))/(y-x(dy)/(dx))=(xcos^2(x^2+y^2))/(y^3)`

A

`tan(x^(2)+y^(2))= x^(2)/y^(2)+c`

B

`cot(x^(2)+y^(2))=x^(2)/y^(2)+c`

C

`tan(x^(2)+y^(2))=y^(2)/x^(2)+c`

D

`cot(x^(2)+y^(2))=y^(2)/x^(2)+c`

Text Solution

Verified by Experts

The given equation can be written as
`(xdx+ydy)/((ydx-xdy)//y^(2))=y^(2)x/y^(3)cos^(2)(x^(2)+y^(2))`
or `(xdx+ydy)/(cos^(2)(x^(2)+y^(2)))=x/y(ydx-xdy)/(y^(2))`
`=1/2sec^(2)(x^(2)+y^(2))d(x^(2)+y^(2))=x/yd(x/y)`
On integrating, we get
`1/2tan(x^(2)+y^(2))=1/2(x/y)^(2)+c/2`
or `tan(x^(2)+y^(2))+c`
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