Multiple choice

Solution of the differential equation $3y \frac{dy}{dx} + 2x$= 0 represents a family of

  1. ellipses

  2. circles

  3. parabolas

  4. hyperbolas

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A Correct answer
Explanation

The equation 3y(dy/dx) + 2x = 0 can be rewritten as 3y dy = -2x dx. Integrating both sides gives 3/2 * y^2 = -x^2 + C, or x^2 + 1.5y^2 = C, which is the standard form of an ellipse.