If the solution of differential equation $\frac{dy}{dx}=\frac{ax +3}{2y+5}$ represents a circle, then $a$ is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → -2
$\frac{dy}{dx}=\frac{ax +3}{2y+5}$
$⇒\int (2y+5)dy=\int (ax +3)dx$
$⇒y^2+5y=\frac{a}{2}x^2+3x+C$
for the equation to represent a circle,
$x^2+y^2+bx+Ey+F=0$
$≡y^2+5y-\frac{a}{2}x^2-3x-C=0$
$⇒-\frac{a}{2}=1$
$⇒a=-2$