Hello!Can you please explain how I should simplify this expression correctly? I am not sure what value belongs in the second box. Thank you for your assistance. **Use the Laplace transform to solve the given initial-value problem.**Given:\[ y'' + y = \delta\left( t - \frac{1}{2} \pi \right) + \delta\left( t - \frac{5}{2} \pi \right), \quad y(0) = 0, \, y'(0) = 0 \]Solution:\[ y(t) = \left( -\cos(t) \right) u\left( t - \frac{\pi}{2} \right) + \cos\left( t - \frac{5\pi}{2} \right) u\left( t - \frac{5\pi}{2} \right) \]There are two parts of the solution:1. \( -\cos(t) \) multiplied by the unit step function \( u\left( t - \frac{\pi}{2} \right) \) - This represents a step function that shifts the cosine function starting at \( t = \frac{\pi}{2} \).2. \( \cos\left( t - \frac{5\pi}{2} \right) \) multiplied by the unit step function \( u\left( t - \frac{5\pi}{2} \right) \) - This starts the cosine function at \( t = \frac{5\pi}{2} \).**Need Help?**If you require additional understanding or guidance on the concept, consider utilizing the assistance feature available.

Name: Hello!Can you please explain how I should simplify this expression cor
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Hello!Can you please explain how I should simplify this expression correctly? I am not sure what value belongs in the second box. Thank you for your assistance. **Use the Laplace transform to solve the given initial-value problem.**Given:\[ y'' + y =