A.8.2: Section 8.2 Answers
( \newcommand{\kernel}{\mathrm{null}\,}\)
1.
- t3e7t2
- 2e2tcos3t
- e−2t4sin4t
- 23sin3t
- tcost
- e2t2sinh2t
- 2te2t3sin9t
- 2e3t3sinh3t
- e2ttcost
2.
- t2e7t+176t3e7t
- e2t(16t3+16t4+140t5)
- e−3t(cos3t+23sin3t)
- 2cos3t+13sin3t
- (1−t)e−t
- cosh3t+13sinh3t
- (1−t−t2−16t3)e−t
- et(2cos2t+52sin2t)
- 1−cost
- 3cosht+4sinht
- 3et+4cos3t+13sin3t
- 3te−2t−2cos2t−3sin2t
3.
- 14e2t−14e−2t−e−t
- 15e−4t−415et+5e3t
- −12e2t−1310e−2t−15e3t
- −25e−4t−35et
- 320e2t−3712e−2t+13et+85e−3t
- 3910et+314e3t+23105e−4t−73e2t
4.
- 45e−2t−12e−t−310cost+1110sint
- 25sint+65cost+75e−tsint−65e−tcost
- 813e2t−813e−tcos2t+1526e−tsin2t
- 12tet+38et+e−2t−118e−3t
- 23tet+19et+te−2t−19e−2t
- −et+52tet+cost−32sint
5.
- 35cos2t+15sin2t−35cos3t−215sin3t
- −415cost+115sint+415cos4t−160sin4t
- 53cost+sint−53cos2t−12sin2t
- −13cost2+23sint2+13cost−13sint
- 115cost4−815sint4−115cos4t+130sin4t
- 25cost3−35sint3−25cost2+25sint2
6.
- et(cos2t+sin2t)−e−t(cos3t+43sin3t)
- e3t(−cos2t+32sin2t)+e−t(cos2t+12sin2t)
- e−2t(18cost+14sint)−e2t(18cos3t−112sin3t)
- e2t(cost+12sint)−e3t(cos2t−14sin2t)
- et(15cost+25sint)−e−t(15cos2t+25sin2t)
- et/2(−cost+98sint)+e−t/2(cost−18sint)
7.
- 1−cost
- et16(1−cos4t)
- 49e2t+59e−tsin3t−49e−tcos3t
- 3et/2−72etsin2t−3etcos2t
- 14e3t−14e−tcos2t
- 19e2t−19e−tcos3t+59e−tsin3t
8.
- −310sint+25cost−34et+720e3t
- −35e−tsint+15e−tcost−12e−t+310et
- −110etsint−710etcost+15e−t+12e2t
- −12et+710e−t−15cos2t+35sin2t
- 310+110e2t+110etsin2t−25etcos2t
- −49e2tcos3t+13e2tsin3t−59e2t+et
9. 1aebatf(ta)