Mathematic Methods HW Solutions 42

Mathematic Methods HW Solutions 42 - Chapter 8 42 y = (Ax +...

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Chapter 8 42 5.30 y = ( Ax + B ) sin x + ( Cx + D ) cos x + ( Ex + F ) e x + ( Gx + H ) e - x 5.34 θ = θ 0 cos ωt , ω = r g/l 5.35 T = 2 π r R/g = 85 min. 5.36 ω = 1 / LC 5.38 overdamped: R 2 C > 4 L ; critically damped: R 2 C = 4 L ; underdamped: R 2 C < 4 L . 5.40 ¨ y + 16 π 15 ˙ y + 4 π 2 9 y = 0, y = e - 8 πt/ 15 p A sin 2 πt 5 + B cos 2 πt 5 P 6.1 y = Ae 2 x + Be - 2 x - 5 2 6.2 y = ( A + Bx ) e 2 x + 4 6.3 y = Ae x + Be - 2 x + 1 4 e 2 x 6.4 y = Ae - x + Be 3 x + 2 e - 3 x 6.5 y = Ae ix + Be - ix + e x 6.6 y = ( A + Bx ) e - 3 x + 3 e - x 6.7 y = Ae - x + Be 2 x + xe 2 x 6.8 y = Ae 4 x + Be - 4 x + 5 xe 4 x 6.9 y = ( Ax + B + x 2 ) e - x 6.10 y = ( A + Bx ) e 3 x + 3 x 2 e 3 x 6.11 y = e - x ( A sin 3 x + B cos3 x ) + 8 sin4 x - 6 cos4 x 6.12 y = e - 2 x [ A sin(2 2 x ) + B cos(2 2 x )] + 5(sin 2 x - cos2 x ) 6.13 y = ( Ax + B ) e x - sin x 6.14 y = e - 2 x ( A sin 3 x + B cos3 x ) - 3 cos5 x 6.15 y = e - 6 x/ 5 [ A sin(8 x/ 5) + B cos(8
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