The image you provided contains some mathematical content that seems to involve a few key equations and a table.

Extracted Content:

1. Equation 1: $f'(t) = - \frac{5}{t^{2}}f(t)$ This equation likely describes a first-order ordinary differential equation (ODE).

2. Equation 2: $f(t) = \frac{k}{t^{5}}$ This appears to be the general solution to the first ODE where $k$ is a constant.

3. Instructions:

   • There is a question or problem statement asking the reader to compare this general solution with another form given specific conditions.
   • The table included suggests that there are some values (or solutions) being compared, likely involving constants $k_1$ and $k_2$ corresponding to different scenarios.

4. Table Description:

   • The table contains results or conditions for different values of $C_{a}$ and $C_{b}$ when $k_1 = 0.1$ and $k_2 = 2.0$.

Steps to Understand and Solve the Problem:

1. Interpret the Differential Equation:

   • Identify what the differential equation represents and how its solution was derived.
   • If the given solution $f(t) = \frac{k}{t^{5}}$ is indeed the general solution, substitute it back into the original ODE to confirm.

2. Compare Solutions:

   • If comparing two solutions (e.g., $k_1$ and $k_2$), analyze how the constants affect the behavior of the solution.
   • Use the table to determine the impact of different $C_a$ and $C_b$ values on the constants.

3. Verification:

   • Verify the solutions by applying initial or boundary conditions if provided or implied by the table.
   • Understand the context of $C_a$ and $C_b$ in relation to the differential equation and its solution.

Would you like a detailed step-by-step analysis of the problem or further clarification on specific aspects?

Related Questions:

1. What is the general method to solve first-order differential equations like the one given?
2. How does changing the constant $k$ affect the general solution $f(t)$?
3. What role do the parameters $C_a$ and $C_b$ play in the problem, based on the table provided?
4. How can the validity of the general solution $f(t) = \frac{k}{t^{5}}$ be confirmed by substitution?
5. How would you apply specific initial conditions to find the exact value of $k$?

Tip: When dealing with differential equations, always check your solution by differentiating and substituting it back into the original equation to ensure it satisfies the equation.