The most general solution of the differential equation `(x+y(dy)/(dx))/(x-y(dx)/(dy))=(2y^(3))/(x^(5))sin^(2)(x^(2)+y^(2))` is

Options

A. `-1/2 cot (x^(2)+y^(2))-(2(y//x)^(4))/4+c=0`
B. `-1/2cot(x^(2)+y^(2))-(2(y//x)^(4))/4+e^(c)=0`
C. `1/2cot(x^(2)+y^(2))-(2(y//x)^(4))/4+tanc=0`
D. `1/4 tan (x^(2)+y^(4))-(2y^(3))/x+c=0`

Answer

A, C

Explanation

`1/2 cosec^(2)(x^(2)+y^(2))d(x^(2)+y^(2))=(y/x)^(2)d(y/x)`
`implies-1/2cot(x^(2)+y^(2))-(2(y//x)^(4))/4+c=0`