- 7 9 Exercises In Problems 1 6 Evaluate The Given Integral 1 1 8 1 2 E 6 1 Di 3 30 8 1 7 In 4 5 6 E 8 1 (52.18 KiB) Viewed 13 times
7.9 EXERCISES In Problems 1-6, evaluate the given integral. 1 (²-1)8(1) 2 [_e³6(1) di 3 [(30) 8 (1-7) in 4. 5. 6. e-²¹8(1+1) di √e ²18(1-1) di Los (cos 21) 8 (1) dt In Problems 7-12, determine the Laplace transform of the given generalized function. 7. 8(1-1)-8(1-3) 8. 38(t-1) 9. 18(1-1) 10. ³8(1-3) 11. 8(1-7)sint 12. ¹8(1-3) In Problems 13-20, solve the given symbolic initial value problem. 13. w"+w=8(1-7); w(0) = 0, w'(0) = 0 14. y" + 2y + 2y = 8(17): y(0) = 1, y'(0) = 1 15. y" + 2y3y y(0) = 2, = 8(1-1)-8(1-2) y' (0) = -2 16. y"-2y'3y = 28(t-1)-8(1-: y(0) = 2, y' (0) = 2 17. y" y = 48(1-2) + 1²; y(0) = 0, y' (0) = 2 18. y"-y'-2y = 38(1-1) +e; y(0) = 0. y' (0) = 3 19. w+6w' +5w = e'8(t-1); w(0) = 0, w' (0) = 4 20. y" + 5y +6y=e¹8(1-2); y(0) = 2, y' (0) = -5 In Problems 21-24, solve the given sym problem and sketch a graph of the solution 21. y"+y = 8(1-2π); y(0) = 0. y' (0) = 1 22. y"+y = 8(t-π/2); y(0) = 0 y' (0) = 1 23. y"+y=-6(1-7)+8(1-27); y' (0) = 1 y(0) = 0, 24. y"+y = 8(1-7)-8(1-2); y' (0) = 1 y(0) = 0.