Linear Equations of Second Order
Math 4430 – Practice Problems – Linear Equations of Second
Order .
1. Find the general solutions of the following equations :
(1) y'' + 3y' + 2y = 4
(2) y'' + 3y' + 2y = 12et
(3) y'' + 3y' + 2y = sin t
(4) y'' + 3y' + 2y = cos t
(5) y'' + 3y' + 2y = 1 + e-t + sin t
(6) y'' − 2y' + 2y = et sin t
(7) y'' − 2y' + y = 6et
(8) y'' + y' + y = t2
(9) y'' + 4y = t sin 2t
(10) y'' + y' = t + sin 2t
(11) 2y'' + 3y' + y = e-3t
(12) y'' + y' = t + sin 2t
2. Solve the following initial value problems using Laplace transform:
(1) y'' + 3y' + 2y = 4; y(0) = 3, y'(0) = 1.
(2) y'' + 3y' + 2y = 4; y(0) = 4, y'(0) = −1.
(3) y'' + 3y' + 2y = et; y(0) = 1, y'(0) = −1.
(4) y'' − 5y' + 6y = et; y(0) = 1, y'(0) = 1.
(5) y'' − y = e2t; y(0) = 0, y'(0) = 1.
(6) y'' − 4y = et; y(0) = 1, y'(0) = 1.
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