Question

If \( x \frac{dy}{dx} = x \cdot f(xy) \), then \( f(xy) \) is equal to?

• A. \( k \cdot e^{x^2} \)
• B. \( k \cdot e^{y^2} \)
• C. \( k \cdot e^{x^y} \)
• D. \( k \cdot e^{y/x} \)

Hint:

Use substitution methods to simplify differential equations involving products or powers of variables.

Answer 1

The Correct Option is A

The given equation can be solved using an appropriate method, and by simplifying the expression, we find that \( f(xy) \) is equal to \( k \cdot e^{x^2} \).