Question

The solution of \( \frac{dy}{dx} = \frac{x^2 + y^2 + 1}{2xy} \), satisfying \( y(1) = 0 \), is given by?

• A. hyperbola
• B. ellipse
• C. circle
• D. parabola

Hint:

The general form of a differential equation involving both \( x^2 \) and \( y^2 \) can lead to a hyperbolic curve.

Answer 1

The Correct Option is A

The given differential equation resembles the standard form of the equation of a hyperbola when solved using the method of separation of variables or a suitable substitution.