Question

The solution of the differential equation \[ (x^2 - yx^2) \frac{dy}{dx} + y^2 + xy^2 = 0 \] is

• A. \( \log \left( \frac{x}{y} \right) = \frac{1}{x} + \frac{1}{y} + C \)
• B. \( \log \left( \frac{x}{y} \right) = \frac{1}{x} + \frac{1}{y} + C \)
• C. \( \log(xy) = \frac{1}{x} + \frac{1}{y} + C \)
• D. \( \log(xy) + \frac{1}{x} + \frac{1}{y} = C \)

Hint:

To solve a differential equation, isolate terms involving \( y \) and \( x \), and integrate both sides.

Answer 1

The Correct Option is C

By solving the given differential equation using standard methods, we obtain \( \log(xy) = \frac{1}{x} + \frac{1}{y} + C \) as the solution.