(t)= -3[y' (t)]³-5 cos (y(t)) + 6e²t (5) y(0)=y'(0)==y(0)=0 Let x₁ = y₁ X₂ = y', X3 = y'', x4 = y(3), x5 = y(4), and x6 = y(5). Complete the differential equation and initial condition for X₁. x₁ (0) = Complete the differential equation and initial condition for X2. x₂ = x₂ (0) = Complete the differential equation and initial condition for X3. X3 X3 (0) = Complete the differential equation and initial condition for X4 X4' = X4 (0) = Complete the differential equation and initial condition for x5. X5' X5 (0) = Complete the differential equation and initial condition for X6- X6' = X6 (0)= ...

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Convert the given initial value problem into an initial value problem for a system in normal form.
y (6) (t) = -3[y'(t)]³-5 cos (y(t)) + 6e²t
y(0) = y'(0) = ... = y(5) (0) = 0
(5)
=y' Complete the differential equation and initial condition for x₁
Let x₁ = y, x₂ = y', x3 =y",
x ₁² =
x₁ (0) =
Complete the differential equation and initial condition for X2
and x6 =
X₂' =
x₂ (0) =
Complete the differential equation and initial condition for X3
x3 =
X3 (0) =
Complete the differential equation and initial condition for X4-
X4' =
X4 (0)=
Complete the differential equation and initial condition for X5
x6 =
X6 (0) =
X5 =
X5 (0) =
Complete the differential equation and initial condition for X6-
G
Transcribed Image Text:Convert the given initial value problem into an initial value problem for a system in normal form. y (6) (t) = -3[y'(t)]³-5 cos (y(t)) + 6e²t y(0) = y'(0) = ... = y(5) (0) = 0 (5) =y' Complete the differential equation and initial condition for x₁ Let x₁ = y, x₂ = y', x3 =y", x ₁² = x₁ (0) = Complete the differential equation and initial condition for X2 and x6 = X₂' = x₂ (0) = Complete the differential equation and initial condition for X3 x3 = X3 (0) = Complete the differential equation and initial condition for X4- X4' = X4 (0)= Complete the differential equation and initial condition for X5 x6 = X6 (0) = X5 = X5 (0) = Complete the differential equation and initial condition for X6- G
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