1. Resolva a equação diferencial dada pelo método dos coeficientes a determinar. (a) y′′ + 3y′ + 2y = 6. Resp: y = c1e−2x + c2e−x + 3 (b) y′′ − 10y...

1. Resolva a equação diferencial dada pelo método dos coeficientes a determinar.
(a) y′′ + 3y′ + 2y = 6. Resp: y = c1e−2x + c2e−x + 3
(b) y′′ − 10y + 25y = 30x + 3. Resp: y = (c1 + c2x)e5x + 3/5
(c) y′′ + y′ + y = x2 − 2x. Resp: y = (c1 + c2x)e−2x + x2 − 4x + 5
(d) y′′ + 3y′ = −48x2e3x. Resp: y = c1 + c2e−3x + (−28/27 + 8x/3 − 8x2/3)e3x
(e) y′′ − y′ = −3. Resp: y = c1 + c2ex + 3x + 3
(f) y′′ − y′ + 1/4 y = 3 + ex/2. Resp y = (c1 + c2x)e^(1/2 x) + 3 + (1/8)x^2e^(1/2 x)
(g) y′′ + 4y = 3 sen 2x. Resp: y = c1 cos (2x) + c2 sen (2x) − 3/4 x cos (2x)
(h) y′′ + y = 2x sen x. Resp: y = c1 cos x + c2 sen x + 1/2 x sen x − 1/2 x^2 cos x