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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
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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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
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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