Find the general solution of the differential equation y" (t) + 36y(t) = 0. %3D general solution = (Use the letters A and B for any constants you have in your solution.) For each of the following initial conditions, find a particular solution. (1) y(0) = 0, y'(0) = 1: y = (ii) y(0) = 1. y' (0) = 0: y = %3D (iii) y(0) = 1, y(1) = 0: y = (iv) y(0) = 0, y(1) = 1: y = %3D %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Find the general solution of the differential equation
y" (t) + 36y(t) = 0.
general solution =
(Use the letters A and B for any constants you have in your solution.)
For each of the following initial conditions, find a particular solution.
(1) y(0) = 0, y'(0) = 1: y =
(ii) y(0) = 1. y' (0) = 0: y =
(iii) y(0) = 1, y(1) = 0: y =
(iv) y(0) = 0, y(1) = 1: y =
Transcribed Image Text:Find the general solution of the differential equation y" (t) + 36y(t) = 0. general solution = (Use the letters A and B for any constants you have in your solution.) For each of the following initial conditions, find a particular solution. (1) y(0) = 0, y'(0) = 1: y = (ii) y(0) = 1. y' (0) = 0: y = (iii) y(0) = 1, y(1) = 0: y = (iv) y(0) = 0, y(1) = 1: y =
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