The image has been opened. I will now analyze the mathematical content to provide solutions to the problem. Let's begin by extracting and solving the questions shown.From the image, the text seems to describe a mathematical problem that involves the derivation of specific equations. However, due to the angle and potential image distortion, I might need more context for certain symbols. Let me summarize what I can clearly interpret, and we can clarify any unknowns together.

1. First Problem (15): It involves the Laplace transform and uses the initial value theorem to solve a problem. It is likely asking for the derivation or the application of the Laplace transform for a specific equation.

2. Second Problem (16): This seems to relate to the calculation of integrals (or transforms) in Laplace form.

Both problems appear to deal with Laplace transforms, differential equations, and potentially boundary conditions. I will try to infer and explain step-by-step how to approach these problems based on common formats.

If you can provide more details on unclear areas, I can refine the solutions further.

Let's start solving each based on these assumptions. Let me know if any clarification is needed. Should I proceed to solve this based on Laplace transforms and initial value problems?