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Find the general solution of a) y"-2y'+ y = e^(λx), where A is a real constant. (Hint: You should consider two cases: A = 1 and λ # 1.) b) y"+y = cos(kx), where k is an integer. (Hint: You should consider two cases: k = ±1 and k 6= ±1.) c) y" −2y' + (2/t)y = 10t (t > 0), y1(t) = t is a solution to the homogeneous part of the equation.

Find the general solution of a) y"-2y'+ y = e^(λx), where A is a real constant. (Hint: You should consider two cases: A = 1 and λ # 1.) b) y"+y = cos(kx), where k is an integer. (Hint: You should consider two cases: k = ±1 and k 6= ±1.) c) y" −2y' + (2/t)y = 10t (t > 0), y1(t) = t is a solution to the homogeneous part of the equation.

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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Find the general solution of a) y"-2y'+ y = e^(^x), where A is a real constant. (Hint: You should consider two cases: A = 1 and λ = 1.) b) y"+ y = cos(kx), where k is an integer. (Hint: You should consider two cases: k = ±1 and k 6= ±1.) c) y" -2y' + (2/t)y = 10t (t > 0), y1(t) = t is a solution to the homogeneous part of the equation.
Transcribed Image Text:Find the general solution of a) y"-2y'+ y = e^(^x), where A is a real constant. (Hint: You should consider two cases: A = 1 and λ = 1.) b) y"+ y = cos(kx), where k is an integer. (Hint: You should consider two cases: k = ±1 and k 6= ±1.) c) y" -2y' + (2/t)y = 10t (t > 0), y1(t) = t is a solution to the homogeneous part of the equation.
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