2. Consider the differential equation -2t?y" +ty' + 5y = g(t), fort> 0. (a) Let g(t) = 0, which makes this differential equation homogenous. If y, = t³ is a solution, find the general solution to this homogeneous differential equation. 7 (b) Now let g(t) = to In(t), which makes this differential equation nonhomogeneous. Find the general solution to this nonhomogeneous equation. You may leave unevaluated definite integrals in your answer.
2. Consider the differential equation -2t?y" +ty' + 5y = g(t), fort> 0. (a) Let g(t) = 0, which makes this differential equation homogenous. If y, = t³ is a solution, find the general solution to this homogeneous differential equation. 7 (b) Now let g(t) = to In(t), which makes this differential equation nonhomogeneous. Find the general solution to this nonhomogeneous equation. You may leave unevaluated definite integrals in your answer.
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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Transcribed Image Text:2. Consider the differential equation –2t?y" +ty' + 5y = g(t), for t > 0.
(a) Let g(t) = 0, which makes this differential equation homogenous. If y1 = t³ is a
solution, find the general solution to this homogeneous differential equation.
7
(b) Now let g(t) = tō In(t), which makes this differential equation nonhomogeneous. Find
the general solution to this nonhomogeneous equation. You may leave unevaluated
definite integrals in your answer.
gle) = {°. lnlt)
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