Question

Solve the third-order initial value problem below using the method of Laplace transforms. y''! + 2y'' – 11y' – 12y = - 48, y(0) = 7, y' (O) = 4, y''(0) = 80 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. y(t)= (Type an exact answer in terms of e.)

Answer 1

The given diffrential equation is y"424" ally'-12y = -48 960)=7 y 10) = 4,4" (0) = 8 Taking laplace transform on both side L {11} +2 L {y" } - 1 l {y } – 12 289} = -48 h {1} where {y!"} = 83 L{Y} - g² y 1o) - gyllo) - y"(0) and L{y"} = 8² L {4} - 5410) - y10 L{y'} = SL{Y}-90) or equation become. [ 3²2{4} = 3²410) - JY'(o)-yt (0)] + 2 [5² L {Y} - sy(0) -Y (0)] - 11 [3L {Y}-460) - 12 L {y} = -484{1} T² RIS) - 98²-45-80] +2 [ 3² R13) - 78 -4] -11[34(3) - 73 - 12413) = -48 (5) given Y" ) = 80, y'(o) = 4, 910)7 - where L{Y} = k18)

[8%+232-13 -12] F13) -8782-48-80-148-8 +77 [88+28° -11 5 –12] F18) – 98-183 -10 = -48 : [ g 3 +28²-113-12] f 13 = -48 + (4 g ² + 18 5+10) +18) -48 - 3(83427² - 118-12 98?+183 +10 23+28²-115-12 fractions techniques using partial We get 819 = 4 HE Hoya 7 50 21 St4 Taking inverse laplace transform of both the sides, we get 13413)3 = 447{}}-442-3113-115319443} +H3+3+ het 1&33+ 1}

* 3418)} = 44-46 484 - 4+ +(4+tuett (4+ na jest +14+ $) ett YH) = 44 - 49 6 + - 143 at +62 est TR2 Hence solve. od 0