Question: Clarifying and Solving a New ODE with Exponential Terms

I am currently working with an ordinary differential equation (ODE) that I find difficult to express and solve accurately. In this ODE, the symbol f represents an exponential function rather than a typical variable, which adds to the confusion. Although I have followed the format used in related research papers, the results I obtain are not satisfactory.

Since this type of ODE is new and somewhat unfamiliar to me, I would greatly appreciate your guidance in:

1. Properly formulating the ODE.

2. Understanding the role of f in the context of exponential functions.

3. Finding the correct and complete solutions.

4. Learning how to clearly present each solution step by step.

Thank you in advance for your support.

AA.mw