Question

Find the function \( f \) which satisfies the equation \( \frac{df}{dx} = 2f \), given that \( f(0) = e^3 \)

• A. \( 2x + 3 \)
• B. \( \log(2x + 3) \)
• C. \( e^{2x+3} \)
• D. \( \frac{x^2}{2} \)

Hint:

For equations of the form \( \frac{df}{dx} = kf \), the solution is always exponential \( f = Ce^{kx} \)Use initial condition to find \( C \).

Answer 1

The Correct Option is C