If the solution of the differential equation
`(dy)/(dx)=(ax+3)/(2y+f)`
represents a circle, then the value of 'a' is

Options

A. 2
B. 1
C. -2
D. -1

Answer

C

Explanation

Given differential equation is
`(dy)/(dx) = (ax +3)/(2y +f)`
By separating the variable we get
(2y +f) dy = (ax +3)dx
Integtrate on both side,
` int (2y +f) dy= int (ax +3) dx`
` Rightarrow y^(2) +fy = (ax^(2))/2 +3x`
This equation represents a circle,if
` -1 = a/2 Rightarrow a=-2`