https://file.aiquickdraw.com/mathbot/file/1725735619249pi66mlf2.jpg

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?

Discover how to apply the Laplace Transform and the Initial Value Theorem to solve complex differential equations. This guide provides a step-by-step approach for university-level students, covering key concepts and formulas needed to master the topic.

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