ODE No. 1894

10.39 ODE No. 1894

${\frac{d^{2}}{d t^{2}} x (t) + a (\frac{d}{d t} x (t) - \frac{d}{d t} y (t)) + b 1 x (t) = c 1 e^{i ω t}, \frac{d^{2}}{d t^{2}} y (t) + a (\frac{d}{d t} y (t) - \frac{d}{d t} x (t)) + b 2 y (t) = c 2 e^{i ω t}}$

Mathematica: cpu = 0 (sec), leaf count = 0 $Hanged$

Maple: cpu = 0.671 (sec), leaf count = 2511 ${{x (t) = \frac{i e^{i ω t} a c 1 ω + i e^{i ω t} a c 2 ω - e^{i ω t} c 1 ω^{2} + e^{i ω t} b 2 c 1}{- 2 i a ω^{3} + i a b 1 ω + i a b 2 ω + ω^{4} - b 1 ω^{2} - b 2 ω^{2} + b 2 b 1} +_C 1 e^{R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 1) t} +_C 2 e^{R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 2) t} +_C 3 e^{R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 3) t} +_C 4 e^{R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 4) t}, y (t) = (\frac{(-_C 4 ω^{4} + 2 i_C 4 a ω^{3} + (b 1 + b 2)_C 4 ω^{2} + (- i b 1 a - i b 2 a)_C 4 ω -_C 4 b 2 b 1) {(R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 4))}^{3}}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a} + \frac{(- 2_C 4 a ω^{4} + 4 i_C 4 a^{2} ω^{3} + (2 a b 1 + 2 b 2 a)_C 4 ω^{2} + (- 2 i a^{2} b 1 - 2 i a^{2} b 2)_C 4 ω - 2_C 4 a b 1 b 2) {(R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 4))}^{2}}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a} + \frac{(-_C 4 b 1 ω^{4} + 2 i_C 4 a b 1 ω^{3} + ({b 1}^{2} + b 2 b 1)_C 4 ω^{2} + (- i a {b 1}^{2} - i a b 1 b 2)_C 4 ω -_C 4 {b 1}^{2} b 2) R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 4)}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a} + \frac{-_C 4 a b 1 ω^{4} + 2 i_C 4 a^{2} b 1 ω^{3} + (a {b 1}^{2} + a b 1 b 2)_C 4 ω^{2} + (- i a^{2} {b 1}^{2} - i a^{2} b 1 b 2)_C 4 ω -_C 4 a {b 1}^{2} b 2}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a}) e^{R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 4) t} + (\frac{(-_C 3 ω^{4} + 2 i_C 3 a ω^{3} + (b 1 + b 2)_C 3 ω^{2} + (- i b 1 a - i b 2 a)_C 3 ω -_C 3 b 2 b 1) {(R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 3))}^{3}}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a} + \frac{(- 2_C 3 a ω^{4} + 4 i_C 3 a^{2} ω^{3} + (2 a b 1 + 2 b 2 a)_C 3 ω^{2} + (- 2 i a^{2} b 1 - 2 i a^{2} b 2)_C 3 ω - 2_C 3 a b 1 b 2) {(R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 3))}^{2}}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a} + \frac{(-_C 3 b 1 ω^{4} + 2 i_C 3 a b 1 ω^{3} + ({b 1}^{2} + b 2 b 1)_C 3 ω^{2} + (- i a {b 1}^{2} - i a b 1 b 2)_C 3 ω -_C 3 {b 1}^{2} b 2) R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 3)}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a} + \frac{-_C 3 a b 1 ω^{4} + 2 i_C 3 a^{2} b 1 ω^{3} + (a {b 1}^{2} + a b 1 b 2)_C 3 ω^{2} + (- i a^{2} {b 1}^{2} - i a^{2} b 1 b 2)_C 3 ω -_C 3 a {b 1}^{2} b 2}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a}) e^{R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 3) t} + (\frac{(-_C 2 ω^{4} + 2 i_C 2 a ω^{3} + (b 1 + b 2)_C 2 ω^{2} + (- i b 1 a - i b 2 a)_C 2 ω -_C 2 b 1 b 2) {(R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 2))}^{3}}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a} + \frac{(- 2_C 2 a ω^{4} + 4 i_C 2 a^{2} ω^{3} + (2 a b 1 + 2 b 2 a)_C 2 ω^{2} + (- 2 i a^{2} b 1 - 2 i a^{2} b 2)_C 2 ω - 2_C 2 a b 1 b 2) {(R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 2))}^{2}}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a} + \frac{(-_C 2 b 1 ω^{4} + 2 i_C 2 a b 1 ω^{3} + ({b 1}^{2} + b 2 b 1)_C 2 ω^{2} + (- i a {b 1}^{2} - i a b 1 b 2)_C 2 ω -_C 2 {b 1}^{2} b 2) R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 2)}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a} + \frac{-_C 2 a b 1 ω^{4} + 2 i_C 2 a^{2} b 1 ω^{3} + (a {b 1}^{2} + a b 1 b 2)_C 2 ω^{2} + (- i a^{2} {b 1}^{2} - i a^{2} b 1 b 2)_C 2 ω -_C 2 a {b 1}^{2} b 2}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a}) e^{R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 2) t} + (\frac{(-_C 1 ω^{4} + 2 i_C 1 a ω^{3} + (b 1 + b 2)_C 1 ω^{2} + (- i b 1 a - i b 2 a)_C 1 ω -_C 1 b 2 b 1) {(R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 1))}^{3}}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a} + \frac{(- 2_C 1 a ω^{4} + 4 i_C 1 a^{2} ω^{3} + (2 a b 1 + 2 b 2 a)_C 1 ω^{2} + (- 2 i a^{2} b 1 - 2 i a^{2} b 2)_C 1 ω - 2_C 1 a b 1 b 2) {(R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 1))}^{2}}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a} + \frac{(-_C 1 b 1 ω^{4} + 2 i_C 1 a b 1 ω^{3} + ({b 1}^{2} + b 2 b 1)_C 1 ω^{2} + (- i a {b 1}^{2} - i a b 1 b 2)_C 1 ω -_C 1 {b 1}^{2} b 2) R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 1)}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a} + \frac{-_C 1 a b 1 ω^{4} + 2 i_C 1 a^{2} b 1 ω^{3} + (a {b 1}^{2} + a b 1 b 2)_C 1 ω^{2} + (- i a^{2} {b 1}^{2} - i a^{2} b 1 b 2)_C 1 ω -_C 1 a {b 1}^{2} b 2}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a}) e^{R o o t O f ({_Z}^{4} + 2 a {_Z}^{3} + (b 1 + b 2) {_Z}^{2} + (a b 1 + b 2 a)_Z + b 2 b 1, i n d e x = 1) t} + \frac{(- a b 2 c 2 ω^{2} + (i a^{2} b 2 c 1 + i a^{2} b 2 c 2) ω + a b 1 b 2 c 2) e^{i ω t}}{(ω^{4} - 2 i a ω^{3} + (- b 1 - b 2) ω^{2} + (i b 1 a + i b 2 a) ω + b 2 b 1) b 2 a}}}$

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