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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 = t_ 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 = t_ is a solution to y" +2y' + 4y = t, find the solution to y" +2y + 4y = 2t-3 cos (2t). (Use part a)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 15CR
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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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