what is the general solution of th differential equation
` (dy)/(dx) +x/y =0` ?

Options

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

Answer

A

Explanation

` (dy)/(dx)+ x/y =0`
` Rightarrow (dy)/(dx) = (-x)/y`
`Rightarrow ydy +x dx =0`
` Rightarrow y^(2)/2 + x^(2)/2 +c =0`
` Rightarrow y^(2) +x^(2) +2c =0`
` Rightarrow x^(2) +y^(2) =c`