Transcribed Image Text: Exercises. Find the general solution given one of the homogeneous solutions. If an initial value is given, solve the IVP. 4 (1)

Transcribed Image Text: Exercises. Find the general solution given one of the homogeneous solutions. If an initial value is given, solve the IVP.
4
(1) /” + ry- =
2i =
(2) a” – ry’ +y = ; 1 = a
(3) ” + 4xy + (4a2 + 2) = 8e-(w+2); =-
(4) a?” + 2.r(a* – 1)y + (a- 2r + 2)y = a2; n = æe”
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3
(5) ” + 2ry – 2y = :(1) =(1) =; = =
(6) (3r – 1),” – (3r +2)/- (6e-8)y = 0; y (0) = 2, y (0) = 3; y = e
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(7) y” + 21y – 2y = 0; =
(8) 4ay” + 2y’ + y = 0; 1 = sin Va
(9) (2 – 2r)y” + (2- )/+ (2- 2)u = 0; y1 = e”
(10) 4a (sin r)y” – 4a(r cos a + sin e)W+ (2r cos r+3 sin æ)y = 0; y1 =
(11) y” + 3ty+y = 0; =-1
(12) (* – 1)y” – ay’+y 0; y1 e”

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