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d²y dx² - y = sinx HINT: For homogenous solution, substitute y = Aex to find roots of characteristic equations r₁= 1 and r2=-1; For particular solution use undetermined coefficients of the form yp-asin(x)+bcos(x). Substitute into original ODE to find a=-1/2 and b=0; ANSWER: y = Ae-x+Bex-1/2sin x

d²y dx² - y = sinx HINT: For homogenous solution, substitute y = Aex to find roots of characteristic equations r₁= 1 and r2=-1; For particular solution use undetermined coefficients of the form yp-asin(x)+bcos(x). Substitute into original ODE to find a=-1/2 and b=0; ANSWER: y = Ae-x+Bex-1/2sin x

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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(8) d²y 2y = sinx dx² HINT: For homogenous solution, substitute y = Aex to find roots of characteristic equations r₁= 1 and r2=-1; For particular solution use undetermined coefficients of the form yp-asin(x)+bcos(x). Substitute into original ODE to find a=-1/2 and b=0; ANSWER: y = Ae-x+Bex-1/2sin x
Transcribed Image Text:(8) d²y 2y = sinx dx² HINT: For homogenous solution, substitute y = Aex to find roots of characteristic equations r₁= 1 and r2=-1; For particular solution use undetermined coefficients of the form yp-asin(x)+bcos(x). Substitute into original ODE to find a=-1/2 and b=0; ANSWER: y = Ae-x+Bex-1/2sin x
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