Question

The solution of the differential equation \( \frac{dx}{dt} = x \log \frac{x}{t} \) is

• A. \( x = e^t \)
• B. \( x + e^t = 0 \)
• C. \( x e^t = 0 \)
• D. \( x = e^t + t \)

Hint:

When solving differential equations, try to separate variables and integrate both sides.

Answer 1

The Correct Option is A

Step 1: Solve the differential equation.
The given equation can be solved using separation of variables, yielding the solution \( x = e^t \). Step 2: Conclusion.
Thus, the correct answer is (A).