Question

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

• A. \( f(x) = y + C \)
• B. \( f(x) = y + C + C \)
• C. \( f(x) = y + C \)
• D. None of the above

Hint:

To solve differential equations, consider using separation of variables and integration techniques.

Answer 1

The Correct Option is B

Step 1: Analyzing the differential equation.
The given equation is separable and can be solved by integrating. The solution to the differential equation yields the form \( f(x) = y + C + C \).

Step 2: Conclusion.
The correct solution is \( f(x) = y + C + C \), corresponding to option (2).