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(2) Linear differential equations with variable coefficient = For each of the following differential equations, find solutions y(t) on [0, ∞) with initial condition y(0) yo. You are wel- come to use whatever method you prefer, but you should clearly communicate what method you are using. (a) y'(t) — cos(t)y(t) = cos(t); (b) y'(t) — ²/₁y(t) = (t + 1)²; (c) y'(t) — ₁y(t) = √t +1

(2) Linear differential equations with variable coefficient = For each of the following differential equations, find solutions y(t) on [0, ∞) with initial condition y(0) yo. You are wel- come to use whatever method you prefer, but you should clearly communicate what method you are using. (a) y'(t) — cos(t)y(t) = cos(t); (b) y'(t) — ²/₁y(t) = (t + 1)²; (c) y'(t) — ₁y(t) = √t +1

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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(2) Linear differential equations with variable coefficient For each of the following differential equations, find solutions y(t) on [0, ∞) with initial condition y(0) = yo. You are wel- come to use whatever method you prefer, but you should clearly communicate what method you are using. (a) y'(t) - cos(t)y(t) = cos(t); (b) y'(t) — ²2/₁y(t) = (t + 1)²; t+1 (c) y'(t) — y(t) = √t +1 2 t+1
Transcribed Image Text:(2) Linear differential equations with variable coefficient For each of the following differential equations, find solutions y(t) on [0, ∞) with initial condition y(0) = yo. You are wel- come to use whatever method you prefer, but you should clearly communicate what method you are using. (a) y'(t) - cos(t)y(t) = cos(t); (b) y'(t) — ²2/₁y(t) = (t + 1)²; t+1 (c) y'(t) — y(t) = √t +1 2 t+1
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