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

Options

A. xy=c
B. x =cy
C. y =cx
D. none of the above

Answer

A

Explanation

` (dy)/(dx) + y/x =0`
` Rightarrow (dy)/(dx) = (-y)/x Rightarrow (dy)/y = - (dx)/x`
` Rightarrow (dy)/y + (dx)/x =0 Rightarrow O (dy)/y = O (dx)/x =0`
` Rightarrow log y + log x = log c`
` Rightarrow log xy= log c`
` Rightarrow xy =c`