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For Problems 1-20, find the Laplace transform of the given function, using Table 5.1 from Section 5.1 and properties of the Laplace transform given in Table 5.2. 1. at² + b + c 2.1² + e²t - 2 3. (t - 9)² 4. e²t - 1 5. (1 + e² 6. 3 t sin t 7. t² sin 2t 8. e-2t sin 3t 9.5 est cos 2t 10. t²e-3t 11. tet cos t 12. t²e¹ sin t 13. sin 2t sinh 2t 14. sin² t 15. sinh 3t 16. cos³t 17. t sin² t

For Problems 1-20, find the Laplace transform of the given function, using Table 5.1 from Section 5.1 and properties of the Laplace transform given in Table 5.2. 1. at² + b + c 2.1² + e²t - 2 3. (t - 9)² 4. e²t - 1 5. (1 + e² 6. 3 t sin t 7. t² sin 2t 8. e-2t sin 3t 9.5 est cos 2t 10. t²e-3t 11. tet cos t 12. t²e¹ sin t 13. sin 2t sinh 2t 14. sin² t 15. sinh 3t 16. cos³t 17. t sin² t

Advanced Engineering Mathematics
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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Help with 17 because the correct answer is (1/2s^2) + (s^2-4 / 2(s^2+4)^2) and i dont know how to get that

**Laplace Transform Problems** **Objective:** For Problems 1–20, determine the Laplace transform of the given function. Utilize Table 5.1 from Section 5.1 and the properties of the Laplace transform found in Table 5.2. 1. \( at^2 + bt + c \) 2. \( t^2 + e^{2t} - 2 \) 3. \( (t - 9)^2 \) 4. \( e^{2t} - 1 \) 5. \( (1 + e^t)^2 \) 6. \( 3t \sin t \) 7. \( t^2 \sin 2t \) 8. \( e^{-2t} \sin 3t \) 9. \( 5 e^{5t} \cos 2t \) 10. \( t e^{-3t} \) 11. \( t e^t \cos t \) 12. \( t^2 e^t \sin t \) 13. \( \sin 2t \sinh 2t \) 14. \( \sin^2 t \) 15. \( \sinh 3t \) 16. \( \cos^3 t \) 17. \( t \sin^2 t \) These exercises aim to apply Laplace transformation techniques to various algebraic and transcendental functions, enabling a deeper understanding of solving differential equations and systems analysis in engineering contexts.
Transcribed Image Text:**Laplace Transform Problems** **Objective:** For Problems 1–20, determine the Laplace transform of the given function. Utilize Table 5.1 from Section 5.1 and the properties of the Laplace transform found in Table 5.2. 1. \( at^2 + bt + c \) 2. \( t^2 + e^{2t} - 2 \) 3. \( (t - 9)^2 \) 4. \( e^{2t} - 1 \) 5. \( (1 + e^t)^2 \) 6. \( 3t \sin t \) 7. \( t^2 \sin 2t \) 8. \( e^{-2t} \sin 3t \) 9. \( 5 e^{5t} \cos 2t \) 10. \( t e^{-3t} \) 11. \( t e^t \cos t \) 12. \( t^2 e^t \sin t \) 13. \( \sin 2t \sinh 2t \) 14. \( \sin^2 t \) 15. \( \sinh 3t \) 16. \( \cos^3 t \) 17. \( t \sin^2 t \) These exercises aim to apply Laplace transformation techniques to various algebraic and transcendental functions, enabling a deeper understanding of solving differential equations and systems analysis in engineering contexts.
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