17] For each of the following equations, • find general solutions; • solve the initial value problem with initial condition y(0) = -1, y'(0) = 2; • sketch the phase portrait, identify the type of each equilibrium, and determine the stability of each equilibrium. %3D (a) 2y" + 9y' + 4y = 0 (b) y" + 2y' – 8y = 0 (c) 4y" – 12y' + 5y = 0

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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[17] For each of the following equations,
• find general solutions;
• solve the initial value problem with initial condition y(0) = –1, y'(0) = 2;
• sketch the phase portrait, identify the type of each equilibrium, and determine the
stability of each equilibrium.
(a) 2y" + 9y' + 4y = 0
(b) у" + 2у - 8у —D0
(с) 4" — 12у + 5у — 0
Transcribed Image Text:[17] For each of the following equations, • find general solutions; • solve the initial value problem with initial condition y(0) = –1, y'(0) = 2; • sketch the phase portrait, identify the type of each equilibrium, and determine the stability of each equilibrium. (a) 2y" + 9y' + 4y = 0 (b) у" + 2у - 8у —D0 (с) 4" — 12у + 5у — 0
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