Question

The particular solution of the differential equation \[ (1 + y^2) \, dx - xy \, dy = 0, \quad y(1) = 0 \quad \text{represents:} \]

• A. a circle
• B. a part of parabola
• C. a part of ellipse
• D. a part of hyperbola

Hint:

To solve differential equations involving initial conditions, apply standard methods of solving such equations, and analyze the form of the solution.

Answer 1

The Correct Option is D

We are given a first-order differential equation and initial conditions. By solving this equation, we find that the solution represents a part of a hyperbola. Thus, the correct answer is option (4).