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3. a) Prove that if y₁ is a solution to the differential equation ay" + by' + cy = fi(t) and Y2 is a solution to ay" +by' + cy=f2(t), then for any constants k₁ and k2, the function kıyı k2y2 is a solution to the differential equation ay" + by' + cy= k₁f1(t) + k₂f2(t). b) Given that y₁ = (1/4) sin(2t) is a solution to y" + 2y' + 4y = cos(2t) and that y2 = is a solution to y" +2y' + 4y = t, find the solution to y" +2y' +4y= 2t-3 cos (2t). (Use part a)

3. a) Prove that if y₁ is a solution to the differential equation ay" + by' + cy = fi(t) and Y2 is a solution to ay" +by' + cy=f2(t), then for any constants k₁ and k2, the function kıyı k2y2 is a solution to the differential equation ay" + by' + cy= k₁f1(t) + k₂f2(t). b) Given that y₁ = (1/4) sin(2t) is a solution to y" + 2y' + 4y = cos(2t) and that y2 = is a solution to y" +2y' + 4y = t, find the solution to y" +2y' +4y= 2t-3 cos (2t). (Use part a)

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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3. a) Prove that if y₁ is a solution to the differential equation ay" +by' + cy = fi(t) and y2 is a solution to ay" +by' + cy=f2(t), then for any constants k₁ and k2, the function kıyı k2y2 is a solution to the differential equation ay"+by' + cy= k₁f1(t) + k₂f2(t). t b) Given that y₁ = (1/4) sin(2t) is a solution to y" + 2y' + 4y = cos(2t) and that y2 = is a solution to y" +2y' + 4y = t, find the solution to y" +2y' + 4y = 2t-3 cos(2t). (Use part a) 4 8
Transcribed Image Text:3. a) Prove that if y₁ is a solution to the differential equation ay" +by' + cy = fi(t) and y2 is a solution to ay" +by' + cy=f2(t), then for any constants k₁ and k2, the function kıyı k2y2 is a solution to the differential equation ay"+by' + cy= k₁f1(t) + k₂f2(t). t b) Given that y₁ = (1/4) sin(2t) is a solution to y" + 2y' + 4y = cos(2t) and that y2 = is a solution to y" +2y' + 4y = t, find the solution to y" +2y' + 4y = 2t-3 cos(2t). (Use part a) 4 8
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