General solution of differential equation `x^(2)(x+y(dy)/(dx))+(x(dy)/(dx)-y)sqrt(x^(2)+y^(2))=0` is

Options

A. `(1)/(sqrt(x^(2)+y^(2)))+(y)/(x)=c`
B. `sqrt(x^(2)+y^(2))-(y)/(x) = c`
C. `sqrt(x^(2)+y^(2))+(y)/(x)=c`
D. `2 sqrt(x^(2)+y^(2))+(y)/(x)=c`

Answer

C

Explanation

`(x dx + y dy)/(sqrt(x^(2)+y^(2)))+(x dy - y dy)/(x^(2))=0`
`rArr" "(1)/(2)(d(x^(2)+y^(2)))/(sqrt(x^(2)+y^(2)))+d((y)/(x))=0`
`rArr" "sqrt(x^(2)+y^(2))+(y)/(x) = c`