can you please show all work as well as all fomulas used thankyou! **Problem 2**Use the Laplace transform to solve the given integral equation.\[f(t) = 2t - 4 \int_{0}^{t} \sin \tau \, f(t-\tau) \, d\tau\]**Explanation**This problem involves solving an integral equation using the Laplace transform. The equation expresses $ f(t) $ as a function of $ t $, subtracting four times the convolution of $ \sin \tau $ with $ f(t-\tau) $. The integral is calculated from 0 to $ t $, with respect to $ \tau $.

Answered: Image /qna-images/answer/b4722682-c97b-45f7-92d0-7a1ee8d3b500.jpg

Answered: 2. Use the Laplace transform to solve…

Math

Advanced Math

2. Use the Laplace transform to solve the given integral equation. f(t) = 2t – 4 sin r f(t – t)dr

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

can you please show all work as well as all fomulas used thankyou!

**Problem 2**

Use the Laplace transform to solve the given integral equation.

\[
f(t) = 2t - 4 \int_{0}^{t} \sin \tau \, f(t-\tau) \, d\tau
\]

**Explanation**

This problem involves solving an integral equation using the Laplace transform. The equation expresses $ f(t) $ as a function of $ t $, subtracting four times the convolution of $ \sin \tau $ with $ f(t-\tau) $. The integral is calculated from 0 to $ t $, with respect to $ \tau $.

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