Which does the solution of the differential equation ` x (dy)/(dx)=y` represent ?

Options

A. family of straight of straight lines through the origin
B. family of circles with their centres at the origin
C. Family of parabolas with their vertices at the origin
D. Family of straight lines having slope 1 and not passing through the origin

Answer

A

Explanation

Given differential equation is
` x(dy)/(dx) =y`
By separating the variables, we get
`(dy)/y= (dx)/x`
Interengrate both the sides, we get
` int (dy)/y = int (dx)/x`
`Rightarrow log y = logx + log c`
` Rightarrow y =xc`
which is a family of straight lines through the origin.