Question

Solve the initial value problem by using La Place:

y 2 y-2u(t - 2n) y(0) 0, y(0)= el-2T

Answer 1

Solution: a) y" +2y'+2y= et-20 (4-20) y (0=0, y colso taking Laplace transform Lay"+2yltzy} = Lof et-zury-ang} Y(8)82-466)8-yło. +2 40578-2YCOJ +278) -208 = SFT substitute ycoiso, y'colo 408) (84728 +21-0-0 = -276 e 8 Y¢8= è 278 (8-1)(8242.862) partial fraction taking we get

- 8- 3 22 2 expanding and rearranging CSf) Yola peste enter teilcom 2 Laplace a inverse taking transform [f4c8l=é C C4-25) - é o moctom) + obet**) U13-20) yele urt-20) (- te behen) - variant -3)tif 2*-37)