Question

Solve listed initial value problems by using the Laplace Transform:

7.       y^ll − y^l − 2y = 3 e^2t     y(0) = −1, y^l(0) = 5

Answer 1

y" - y. 24 cze²t you cut y'10125 Apply lapláce transformia Lly"} - L{4'} - ; 2 L4 y} 3L4: e2tę 8²418) - sy'(o) - syco) - {S410-410)} =2418) _: 8-2 Y(A) 82-8.-2.4 -8.406) -867) +47) 730 1187 (8²-8-2) - sst s t :: 3 82 itsisi 8-2

yol (8 1268-2). E :3 +48 +! L á ? +482-88 +8-2 _ 8-2 st r . 482- 7.8t 1 , 8-2 YA12 482-78th ...18+Ij487242. By partial fraction :- 481-78+).. A + B (8+1) (8-2) 2 i8+1) ($-2) (8-2) ? 48²_78+) Ā (A-21² f Bldf) (8-2) + elst! & but 8=2 '16-14 El ime (241) 1BEBO [(el put say 4 +7+1 Al-312 629AE. Az 12 E Companing Coeff. of s 42 A +B7 B= 4 4 4 = 8/3 Tea Teacher's Signature..

Yis)= 94. - t 8.l t 318+) 3 18-2) (8-2)² taking inuense laplace trains fourni - 1$ 4.033 Y 1) = 641-1644.+ _14(.2)+ y 15-2)2 ] = 4 et + h ezt & teet B e 2t & teet 3