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this is a differential equation question please solve them with steps and details also, make sure...

this is a differential equation question


please solve them with steps and details also, make sure it is correct

2. (4 points each) Find the particular solutions for the following differential equations. (a) y – 4y = 21 (b) y +9y = sec

2. (4 points each) Find the particular solutions for the following differential equations. (a) y" – 4y = 21 (b) y" +9y = sec 3t tan 3t
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Answer #1

2. (a) 2t 27 y - 49 at 6 - AD) Y 2t e P. I. = go ² - 4D at 1 2² - 4.2 at tult (t) YpC Hence particular solution = 2t helt е(b) y tay Auxiliary = Sec (31) tan (30) equation m² +9=0 m = 73 e Sin (3) - ya y = cos(at) y o Ya 7₂ Sin (3) Cos (3+) 3 CosatCos(3+) 3 ( [sec (16) - 1] at In Coscatel + sin (31) 3 3 tan (3t t Cos (3t) 3 3 Sin (3t) en Cosat! 3 t cos (34) 18p Sin(3t+ 9

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