The given differential equation is already in standard form, as the coefficient of the highest order derivative is 1. y" + 3y + 2y = The next Wronskians to calculate use y₁ = ex and y₂ = e-2x that we identified from the complementary function and the function of x that makes the equation nonhomogeneous, f(x) = 4+ex 4 + e W₁ = - 1/80) 3/²/₂/ W₂ 0 = |(4 + 2x)=1 e-2x (4 + ex)-1 -2e-2x = Y₁ 4 + ex e-x 0 -e-x (4 + ex)-¹|
The given differential equation is already in standard form, as the coefficient of the highest order derivative is 1. y" + 3y + 2y = The next Wronskians to calculate use y₁ = ex and y₂ = e-2x that we identified from the complementary function and the function of x that makes the equation nonhomogeneous, f(x) = 4+ex 4 + e W₁ = - 1/80) 3/²/₂/ W₂ 0 = |(4 + 2x)=1 e-2x (4 + ex)-1 -2e-2x = Y₁ 4 + ex e-x 0 -e-x (4 + ex)-¹|
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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Transcribed Image Text:The given differential equation is already in standard form, as the coefficient of the highest order derivative is 1.
1
4 + ex
The next Wronskians to calculate use y₁ = e-X and Y₂ = e-2x that we identified from the complementary function and the function of x that makes the equation nonhomogeneous, f(x)
W₁ =
1
W₂
=
0
= 1 (4 + 2x)
=
y" + 3y' + 2y =
0
Y2
f(x) y'₂
=
e-2x
(4 + ex)-1 -2e-2x
= |
Y₁ 0
Y₁' f(x)
0
-e-x (4 + ex)-1|
e-x
=
1
4 + ex
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