Question

The solution of the differential equation \[ \frac{dy}{dx}(x - y^3) = 0 \] is

• A. \( y = x^3 + C \)
• B. \( y = x^3 + C \)
• C. \( y = 4x^3 + C \)
• D. \( y = 3x^3 + C \)

Hint:

When solving first-order differential equations, separate variables to integrate both sides.

Answer 1

The Correct Option is C

Step 1: Solve the given differential equation.
The given equation can be solved by separating variables and integrating both sides. The solution gives \( y = 4x^3 + C \).

Step 2: Conclusion.
Thus, the correct answer is option (C).

Final Answer: \[ \boxed{\text{(C) } y = 4x^3 + C} \]