**Problem Statement**Solve the initial value problem below using the method of Laplace transforms.\[y'' - 36y = 144t - 36e^{-6t}, \quad y(0) = 0, \quad y'(0) = 47\][Click here to view the table of Laplace transforms.](#)[Click here to view the table of properties of Laplace transforms.](#)**Solution Format**y(t) = \_\_\_\_*(Type an exact answer in terms of $e$.)***Instructions**Use the provided links to view the tables of Laplace transforms and their properties, which will assist in solving the differential equation.

The differential equation is y''-36y=144t-36e-6t, y0=0 and y'0=47. Apply Laplace transforms:…

Answered: Solve the initial value problem below…

Solve the initial value problem below using the method of Laplace transforms. – 6t y" - 36y = 144t – 36 e -6", y(0) = 0, y'(0) = 47

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**Problem Statement**

Solve the initial value problem below using the method of Laplace transforms.

\[
y'' - 36y = 144t - 36e^{-6t}, \quad y(0) = 0, \quad y'(0) = 47
\]

[Click here to view the table of Laplace transforms.](#)

[Click here to view the table of properties of Laplace transforms.](#)

**Solution Format**

y(t) = \_\_\_\_

*(Type an exact answer in terms of $e$.)*

**Instructions**

Use the provided links to view the tables of Laplace transforms and their properties, which will assist in solving the differential equation.

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