Question

Please answer the blamnks. Thank you.

(1 point) Use the Laplace transform to solve the following initial value problem: y6y9y 0,with y(0) 1, y (0) = -4 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)} find the equation you get by taking the Laplace transform of the differential equation =0 Now solve for Y(s) = and write the above answer in its partial fraction decomposition, A Y(s) (s+a} s+a Y(s) Now by inverting the transform, find y(t)

Answer 1

a y"+(-6)y' +gyzo y,0)=1 ,yllo)=ry y"-by'rgyzo 1910)=1 ,y'(o)=-4 Take Laplace on both side Ily") -69 141)+2294)=0. Now a ly")=g²)(B) -13 710) -910) = s? YCB) - 8 +4 Qey')= B YOD) - y10) b yen)-1 then )-ht4-63 y 15) + ) +9YS). 15-60+9) 7(b) – 5+5=0 > 18265+9) YID) = 5+5 S- 5 ) s²613+9 B-5 > yva 15-3) 2 bet B 6-5 A 15 - 3)2 +15-3) tu (5-3)

6-5= A (5-3) + B for rood 873 3-5 =A-O+B > 11=-2] = 3-5= AB-3A+B thon Take inverse Yaplace we get (800) = 316--214-) te at yet)= e 3 ut