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Mathematics LibreTexts

11.51: A.8.2- Section 8.2 Answers

( \newcommand{\kernel}{\mathrm{null}\,}\)

1.

  1. t3e7t2
  2. 2e2tcos3t
  3. e2t4sin4t
  4. 23sin3t
  5. tcost
  6. e2t2sinh2t
  7. 2te2t3sin9t
  8. 2e3t3sinh3t
  9. e2ttcost

2.

  1. t2e7t+176t3e7t
  2. e2t(16t3+16t4+140t5)
  3. e3t(cos3t+23sin3t)
  4. 2cos3t+13sin3t
  5. (1t)et
  6. cosh3t+13sinh3t
  7. (1tt216t3)et
  8. et(2cos2t+52sin2t)
  9. 1cost
  10. 3cosht+4sinht
  11. 3et+4cos3t+13sin3t
  12. 3te2t2cos2t3sin2t

3.

  1. 14e2t14e2tet
  2. 15e4t415et+5e3t
  3. 12e2t1310e2t15e3t
  4. 25e4t35et
  5. 320e2t3712e2t+13et+85e3t
  6. 3910et+314e3t+23105e4t73e2t

4.

  1. 45e2t12et310cost+1110sint
  2. 25sint+65cost+75etsint65etcost
  3. 813e2t813etcos2t+1526etsin2t
  4. 12tet+38et+e2t118e3t
  5. 23tet+19et+te2t19e2t
  6. et+52tet+cost32sint

5.

  1. 35cos2t+15sin2t35cos3t215sin3t
  2. 415cost+115sint+415cos4t160sin4t
  3. 53cost+sint53cos2t12sin2t
  4. 13cost2+23sint2+13cost13sint
  5. 115cost4815sint4115cos4t+130sin4t
  6. 25cost335sint325cost2+25sint2

6.

  1. et(cos2t+sin2t)et(cos3t+43sin3t)
  2. e3t(cos2t+32sin2t)+et(cos2t+12sin2t)
  3. e2t(18cost+14sint)e2t(18cos3t112sin3t)
  4. e2t(cost+12sint)e3t(cos2t14sin2t)
  5. et(15cost+25sint)et(15cos2t+25sin2t)
  6. et/2(cost+98sint)+et/2(cost18sint)

7.

  1. 1cost
  2. et16(1cos4t)
  3. 49e2t+59etsin3t49etcos3t
  4. 3et/272etsin2t3etcos2t
  5. 14e3t14etcos2t
  6. 19e2t19etcos3t+59etsin3t

8.

  1. 310sint+25cost34et+720e3t
  2. 35etsint+15etcost12et+310et
  3. 110etsint710etcost+15et+12e2t
  4. 12et+710et15cos2t+35sin2t
  5. 310+110e2t+110etsin2t25etcos2t
  6. 49e2tcos3t+13e2tsin3t59e2t+et

9. 1aebatf(ta)


This page titled 11.51: A.8.2- Section 8.2 Answers is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by William F. Trench.

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