Question

The particular solution of the differential equation $(1+y^{2})dx-xy \, dy=0$ at $x=1$, $y=0$, represents

• A. circle
• B. pair of straight lines
• C. hyperbola
• D. ellipse

Hint:

Logic Tip: Equations of the form $x^2 + y^2 = a^2$ represent circles, $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ represent ellipses, and $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ represent hyperbolas. Since the signs on the $x^2$ and $y^2$ terms are opposite, it must be a hyperbola.

Answer 1

The Correct Option is C