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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 + bt+c 2.1²+ e²t-2 3. (1-9)² 4. e²1-1 5. (1 + ¹)² 6. 3 t sin t 7. t² sin 2t 8. e-2¹ 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 + bt+c 2.1²+ e²t-2 3. (1-9)² 4. e²1-1 5. (1 + ¹)² 6. 3 t sin t 7. t² sin 2t 8. e-2¹ 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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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. \( at^2 + bt + c \) 2. \( t^2 + e^{2t} - 2 \) 3. \( (t - 9)^2 \) 4. \( e^{2t} - 1 \) 5. \( (1 + e^t)^2 \) 6. \( 3 \, t \sin t \) 7. \( t^2 \sin 2t \) 8. \( e^{-2t} \sin 3t \) 9. \( 5 \, e^5t \cos 2t \) 10. \( t^2 e^{-3t} \) 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. \( t \sin^2 t \) (Note: No graphs or diagrams are present in the image.)
Transcribed Image Text: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. \( at^2 + bt + c \) 2. \( t^2 + e^{2t} - 2 \) 3. \( (t - 9)^2 \) 4. \( e^{2t} - 1 \) 5. \( (1 + e^t)^2 \) 6. \( 3 \, t \sin t \) 7. \( t^2 \sin 2t \) 8. \( e^{-2t} \sin 3t \) 9. \( 5 \, e^5t \cos 2t \) 10. \( t^2 e^{-3t} \) 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. \( t \sin^2 t \) (Note: No graphs or diagrams are present in the image.)
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