Convert the given initial value problem into an initial value problem for a system in normal form. y (6)
(t)=−5[y ′
(t)] 4
−5cos(y(t))+8e 2t
y(0)=y ′
(0)=⋯=y (5)
(0)=0
​
Let x 1
​
=y,x 2
​
=y ′
,x 3
​
=y ′′
,x 4
​
=y (3)
,x 5
​
=y (4)
, and x 8
​
=y (5)
. Complete the differential equation and initial condition for x 1
​
. x 1
​
′
=
x 1
​
(0)=
​
Complete the differential equation and initial condition for x 2
​
. x 2
​
′
=
x 2
​
(0)=
​
Complete the differential equation and initial condition for x 3
​
. x 3
​
′
=
x 3
​
(0)=
​
Complete the differential equation and initial condition for x 4
​
. x 4
​
′
=
x 4
​
(0)=
​
Complete the differential equation and initial condition for x 5
​
. x 5
​
′
=
x 5
​
(0)=
​
Complete the differential equation and initial condition for x 8
​
. x 6
′
​
=
x 6
​
(0)=
​
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