7.(i) Consider the following second order linear differential equation y"(t) +a1 y (t) + az y = b where a1, a2, b are all constants. Discuss the nature of the general solution (y) when a12> 4 a2 and a1? 4 az (ii) Solve the following differential equations when y(0) = 4, y'(0) = 2. (a) y"(t) +3 y' (t) - 4 y = 12 %3D (b) y"(t) +6 y' (t) + 9 y = 27
7.(i) Consider the following second order linear differential equation y"(t) +a1 y (t) + az y = b where a1, a2, b are all constants. Discuss the nature of the general solution (y) when a12> 4 a2 and a1? 4 az (ii) Solve the following differential equations when y(0) = 4, y'(0) = 2. (a) y"(t) +3 y' (t) - 4 y = 12 %3D (b) y"(t) +6 y' (t) + 9 y = 27
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:7.(i) Consider the following second order linear differential equation
y"(t) +ai y (t) + az y = b
where a1, a2, b are all constants. Discuss the nature of the general solution (y)
when a12 > 4 az and a12 4 az
(ii) Solve the following differential equations when y(0) = 4, y'(0) = 2.
(a) y"(t) +3 y' (t) - 4 y = 12
(b) y"(t) +6 y' (t) + 9 y 27
%3D
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