Question

If the solution of the differential equation $\frac{dy}{dx}$ = $\frac{ax + 3}{2y + ƒ}$ represents a circle, then the value of 'a' is –

• A. 2
• B. –2
• C. 3
• D. –4

Answer 1

Answer: (B)

–2

Answer 2

We have, $\frac{dy}{dx}$ = $\frac{ax + 3}{2y + ƒ}$

Ž (ax + 3) dx = (2y + ƒ) dy

On integrating, we obtain

a $\frac{x^{2}}{2}$ + 3x = y² + ƒy + c

Ž – $\frac{a}{2}$ x² + y² – 3x + ƒy + c = 0

This will represent a circle, if

– $\frac{a}{2}$ = 1 [Q Coeff. of x² = Coeff. of y²]

and $\frac{9}{4}$ + ƒ² – c > 0 [Using g² + ƒ² – c > 0]

Ž a = –2 and 9 + 4ƒ² – 4c > 0

Hence (2) is the correct answer