\[ \boxed { \left \{ {\frac {\rm d}{{\rm d}t}}{\it x1} \left ( t \right ) =a{\it x2} \left ( t \right ) +b{\it x3} \left ( t \right ) \cos \left ( ct \right ) +b{\it x4} \left ( t \right ) \sin \left ( ct \right ) ,{\frac {\rm d}{{\rm d}t}}{\it x2} \left ( t \right ) =-a{\it x1} \left ( t \right ) +b{\it x3} \left ( t \right ) \sin \left ( ct \right ) -b{\it x4} \left ( t \right ) \cos \left ( ct \right ) ,{\frac {\rm d}{{\rm d}t}}{\it x3} \left ( t \right ) =-b{\it x1} \left ( t \right ) \cos \left ( ct \right ) -b{\it x2} \left ( t \right ) \sin \left ( ct \right ) +a{\it x4} \left ( t \right ) ,{\frac {\rm d}{{\rm d}t}}{\it x4} \left ( t \right ) =-b{\it x1} \left ( t \right ) \sin \left ( ct \right ) +b{\it x2} \left ( t \right ) \cos \left ( ct \right ) -a{\it x3} \left ( t \right ) \right \} } \]
Mathematica: cpu = 0.011001 (sec), leaf count = 122 \[ \text {DSolve}\left [\left \{\text {x1}'(t)=a \text {x2}(t)+b \text {x3}(t) \cos (c t)+b \text {x4}(t) \sin (c t),\text {x2}'(t)=-a \text {x1}(t)+b \text {x3}(t) \sin (c t)-b \text {x4}(t) \cos (c t),\text {x3}'(t)=a \text {x4}(t)-b \text {x1}(t) \cos (c t)-b \text {x2}(t) \sin (c t),\text {x4}'(t)=-a \text {x3}(t)-b \text {x1}(t) \sin (c t)+b \text {x2}(t) \cos (c t)\right \},\{\text {x1}(t),\text {x2}(t),\text {x3}(t),\text {x4}(t)\},t\right ] \]
Maple: cpu = 1.716 (sec), leaf count = 11399 \[ \left \{ \left \{ {\it x1} \left ( t \right ) ={\it \_C2}+{\it \_C3}\, \sin \left ( ct \right ) +{\it \_C4}\,\cos \left ( ct \right ) ,{\it x2} \left ( t \right ) =\sin \left ( ct \right ) {\it \_C4}-\cos \left ( ct \right ) {\it \_C3}+{\it \_C1},{\it x3} \left ( t \right ) =-{\frac {b \left ( \sin \left ( ct \right ) {\it \_C2}\,a-\cos \left ( ct \right ) { \it \_C1}\,a+{\it \_C3}\,a+{\it \_C3}\,c \right ) }{a \left ( a+c \right ) }},{\it x4} \left ( t \right ) ={\frac {b \left ( \sin \left ( ct \right ) {\it \_C1}\,a+\cos \left ( ct \right ) {\it \_C2}\,a+{\it \_C4} \,a+{\it \_C4}\,c \right ) }{a \left ( a+c \right ) }} \right \} , \left \{ {\it x1} \left ( t \right ) ={\it \_C1}\,{{\rm e}^{-{\frac {t}{ 2}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {{c}^{2} \left ( 4\,{a}^{2}+4\,ac+4\,{b}^{2}+{c}^{2} \right ) }}}}}+{\it \_C2}\, {{\rm e}^{{\frac {t}{2}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}- 2\,\sqrt {{c}^{2} \left ( 4\,{a}^{2}+4\,ac+4\,{b}^{2}+{c}^{2} \right ) } }}}}+{\it \_C3}\,{{\rm e}^{-{\frac {t}{2}\sqrt {-4\,{a}^{2}-4\,ac-4\,{ b}^{2}-2\,{c}^{2}+2\,\sqrt {{c}^{2} \left ( 4\,{a}^{2}+4\,ac+4\,{b}^{2} +{c}^{2} \right ) }}}}}+{\it \_C4}\,{{\rm e}^{{\frac {t}{2}\sqrt {-4\,{ a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {{c}^{2} \left ( 4\,{a}^{2} +4\,ac+4\,{b}^{2}+{c}^{2} \right ) }}}}},{\it x2} \left ( t \right ) =-{ \frac {1}{8\,c \left ( {a}^{2}+ac+{b}^{2} \right ) } \left ( {\it \_C3}\, \left ( -4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c }^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}} \right ) ^{{\frac {3}{2}}} {{\rm e}^{-{\frac {t}{2}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2} +2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}}} }-{\it \_C4}\, \left ( -4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\, \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}} \right ) ^{{\frac {3}{2}}}{{\rm e}^{{\frac {t}{2}\sqrt {-4\,{a}^{2}-4 \,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\, {c}^{2}{b}^{2}+{c}^{4}}}}}}+4\,{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,a c-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c} ^{2}{b}^{2}+{c}^{4}}}t}}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2} +2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{ \it \_C3}\,{a}^{2}+4\,{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^ {2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{ 2}+{c}^{4}}}t}}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\, \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{\it \_C3}\,ac+4\,{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c }^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4 }}}t}}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^ {2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{\it \_C3}\,{b}^{2}+ 4\,{c}^{2}{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{ 2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}} t}}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2} {c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{\it \_C3}-4\,{{\rm e}^ {1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^ {2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}\sqrt {-4\,{a}^{2 }-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+ 4\,{c}^{2}{b}^{2}+{c}^{4}}}{\it \_C4}\,{a}^{2}-4\,{{\rm e}^{1/2\, \sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c} ^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}\sqrt {-4\,{a}^{2}-4\,a c-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c} ^{2}{b}^{2}+{c}^{4}}}{\it \_C4}\,ac-4\,{{\rm e}^{1/2\,\sqrt {-4\,{a}^{ 2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3} +4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\, {c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^ {4}}}{\it \_C4}\,{b}^{2}-4\,{c}^{2}{{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4 \,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\, {c}^{2}{b}^{2}+{c}^{4}}}t}}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^ {2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}} }{\it \_C4}+{\it \_C1}\, \left ( -4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2 }-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}} \right ) ^{{\frac {3}{2}}}{{\rm e}^{-{\frac {t}{2}\sqrt {-4\,{a}^{2}-4 \,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\, {c}^{2}{b}^{2}+{c}^{4}}}}}}-{\it \_C2}\, \left ( -4\,{a}^{2}-4\,ac-4\,{ b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b }^{2}+{c}^{4}} \right ) ^{{\frac {3}{2}}}{{\rm e}^{{\frac {t}{2}\sqrt { -4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4 \,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}}}}+4\,\sqrt {-4\,{a}^{2}-4\,ac- 4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{ 2}{b}^{2}+{c}^{4}}}{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2} -2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+ {c}^{4}}}t}}{\it \_C1}\,{a}^{2}+4\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2} -2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+ {c}^{4}}}{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2 }-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t }}{\it \_C1}\,ac+4\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\, \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{ {\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\, \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{ \it \_C1}\,{b}^{2}+4\,{c}^{2}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c }^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4 }}}{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\, \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{ \it \_C1}-4\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt { 4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{{\rm e}^{1/2 \,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{ c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C2}\,{a}^{2}-4 \,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{ c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{{\rm e}^{1/2\,\sqrt {-4 \,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a {c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C2}\,ac-4\,\sqrt {-4\,{a} ^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{ 3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac- 4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{ 2}{b}^{2}+{c}^{4}}}t}}{\it \_C2}\,{b}^{2}-4\,{c}^{2}\sqrt {-4\,{a}^{2} -4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4 \,{c}^{2}{b}^{2}+{c}^{4}}}{{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{ b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b }^{2}+{c}^{4}}}t}}{\it \_C2} \right ) },{\it x3} \left ( t \right ) ={ \frac {1}{8\,bc \left ( {a}^{2}+ac+{b}^{2} \right ) } \left ( - \left ( -4 \,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a {c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}} \right ) ^{{\frac {3}{2}}}\cos \left ( ct \right ) {{\rm e}^{{\frac {t}{2}\sqrt {-4\,{a}^{2}-4\,ac-4\, {b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{ b}^{2}+{c}^{4}}}}}}{\it \_C2}\,a+4\,\sin \left ( ct \right ) {{\rm e}^{1 /2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2 }{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}\sqrt {4\,{a}^{2}{c }^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}{\it \_C2}\,{a}^{2}+ \left ( -4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c }^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}} \right ) ^{{\frac {3}{2}}} \cos \left ( ct \right ) {{\rm e}^{-{\frac {t}{2}\sqrt {-4\,{a}^{2}-4\,a c-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c} ^{2}{b}^{2}+{c}^{4}}}}}}{\it \_C1}\,a+4\,\sin \left ( ct \right ) \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}{{\rm e}^{-1/ 2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2} {c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C1}\,{a}^{2}- 4\,\sin \left ( ct \right ) {{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\, {b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{ b}^{2}+{c}^{4}}}t}}\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^ {2}+{c}^{4}}{\it \_C3}\,{a}^{2}+\cos \left ( ct \right ) {{\rm e}^{-{ \frac {t}{2}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4 \,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}}}} \left ( -4 \,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a {c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}} \right ) ^{{\frac {3}{2}}}{\it \_C3} \,a+4\,\cos \left ( ct \right ) {{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac -4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^ {2}{b}^{2}+{c}^{4}}}t}}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+ 2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{ \it \_C3}\,{a}^{3}-\cos \left ( ct \right ) {{\rm e}^{{\frac {t}{2} \sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c} ^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}}}} \left ( -4\,{a}^{2}-4\, ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c }^{2}{b}^{2}+{c}^{4}} \right ) ^{{\frac {3}{2}}}{\it \_C4}\,a-4\,\cos \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}- 2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{ c}^{4}}}t}}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4 \,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{\it \_C4}\,{a }^{3}+8\,\sin \left ( ct \right ) {{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\, ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c }^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C1}\,{a}^{3}c+4\,{b}^{2}{c}^{2}{ {\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\, \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{ \it \_C3}\,\sin \left ( ct \right ) +4\,{b}^{2}{c}^{2}{{\rm e}^{1/2\, \sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c} ^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C2}\,\sin \left ( ct \right ) +4\,{b}^{2}{c}^{2}{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2 }-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+ 4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C1}\,\sin \left ( ct \right ) +4\,{ b}^{2}{c}^{2}{{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c} ^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4} }}t}}{\it \_C4}\,\sin \left ( ct \right ) +4\,{b}^{2}\sqrt {4\,{a}^{2}{c }^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}{{\rm e}^{-1/2\,\sqrt {-4 \,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a {c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C1}\,\sin \left ( ct \right ) -4\,{b}^{2}{{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2} -2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+ {c}^{4}}}t}}\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c} ^{4}}{\it \_C4}\,\sin \left ( ct \right ) -4\,{b}^{2}{{\rm e}^{-1/2\, \sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c} ^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}\sqrt {4\,{a}^{2}{c}^{2 }+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}{\it \_C3}\,\sin \left ( ct \right ) +4\,{b}^{2}{{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2} -2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+ {c}^{4}}}t}}\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c} ^{4}}{\it \_C2}\,\sin \left ( ct \right ) +4\,\sqrt {-4\,{a}^{2}-4\,ac-4 \,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2 }{b}^{2}+{c}^{4}}}\cos \left ( ct \right ) {{\rm e}^{-1/2\,\sqrt {-4\,{a }^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^ {3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C1}\,{a}^{3}-4\,\sin \left ( c t \right ) {{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2 }+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t }}\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}{\it \_C4}\,{a}^{2}-4\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\, \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}\cos \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}- 2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{ c}^{4}}}t}}{\it \_C2}\,{a}^{3}+8\,{b}^{2}\sin \left ( ct \right ) { {\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\, \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{ \it \_C1}\,ac+8\,{b}^{2}\sin \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {- 4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\, a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C2}\,ac+8\,{b}^{2}\sin \left ( ct \right ) {{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2} -2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+ {c}^{4}}}t}}{\it \_C3}\,ac+8\,{b}^{2}\sin \left ( ct \right ) {{\rm e}^{ 1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{ 2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C4}\,ac+4\, \sin \left ( ct \right ) \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2} {b}^{2}+{c}^{4}}{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2 \,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c }^{4}}}t}}{\it \_C1}\,ac+4\,\sin \left ( ct \right ) {{\rm e}^{1/2\, \sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c} ^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}\sqrt {4\,{a}^{2}{c}^{2 }+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}{\it \_C2}\,ac+4\,{b}^{2}{ {\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\, \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}} \sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c} ^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{\it \_C3}\,a\cos \left ( c t \right ) -4\,{b}^{2}{{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2 }-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2} +{c}^{4}}}t}}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt { 4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{\it \_C4}\,a \cos \left ( ct \right ) -4\,{b}^{2}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}- 2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{ c}^{4}}}{{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}- 2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}} {\it \_C2}\,a\cos \left ( ct \right ) -4\,{\it \_C3}\,\sqrt {-4\,{a}^{2} -4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4 \,{c}^{2}{b}^{2}+{c}^{4}}}{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\, {b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{ b}^{2}+{c}^{4}}}t}}{b}^{2}c\cos \left ( ct \right ) -4\,{\it \_C1}\,{ {\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\, \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}} \sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c} ^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{b}^{2}c\cos \left ( ct \right ) +4\,{\it \_C2}\,{{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b }^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b} ^{2}+{c}^{4}}}t}}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\, \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{b}^{2 }c\cos \left ( ct \right ) +4\,{\it \_C4}\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{ b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b }^{2}+{c}^{4}}}{{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{ c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{ 4}}}t}}{b}^{2}c\cos \left ( ct \right ) -4\,\sin \left ( ct \right ) { {\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\, \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}} \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}{\it \_C3}\,ac-4\,\sin \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}- 4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4 \,{c}^{2}{b}^{2}+{c}^{4}}}t}}\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{ c}^{2}{b}^{2}+{c}^{4}}{\it \_C4}\,ac+12\,{c}^{2}\sin \left ( ct \right ) {{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2 }-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t }}{\it \_C1}\,{a}^{2}+4\,{c}^{3}\sin \left ( ct \right ) {{\rm e}^{-1/2 \,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{ c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C1}\,a+8\,\sin \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}- 2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{ c}^{4}}}t}}{\it \_C2}\,{a}^{3}c+12\,{c}^{2}\sin \left ( ct \right ) { {\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C2 }\,{a}^{2}+4\,{c}^{3}\sin \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4\, {a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c }^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C2}\,a+8\,\sin \left ( ct \right ) {{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2 }+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t }}{\it \_C3}\,{a}^{3}c+12\,{c}^{2}\sin \left ( ct \right ) {{\rm e}^{-1/ 2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2} {c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C3}\,{a}^{2}+ 4\,{c}^{3}\sin \left ( ct \right ) {{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4 \,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\, {c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C3}\,a+8\,\sin \left ( ct \right ) { {\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C4 }\,{a}^{3}c+12\,{c}^{2}\sin \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4 \,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a {c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C4}\,{a}^{2}+4\,{c}^{3} \sin \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^ {2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{ 2}+{c}^{4}}}t}}{\it \_C4}\,a+4\,{b}^{2}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b} ^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^ {2}+{c}^{4}}}{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c }^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4 }}}t}}{\it \_C1}\,a\cos \left ( ct \right ) \right ) },{\it x4} \left ( t \right ) ={\frac {1}{8\,bc \left ( {a}^{2}+ac+{b}^{2} \right ) } \left ( -4\,{b}^{2}{c}^{2}{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}- 2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{ c}^{4}}}t}}{\it \_C1}\,\cos \left ( ct \right ) -4\,{b}^{2}{c}^{2}{ {\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C4 }\,\cos \left ( ct \right ) -4\,{b}^{2}{c}^{2}{{\rm e}^{-1/2\,\sqrt {-4 \,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a {c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C3}\,\cos \left ( ct \right ) -4\,{b}^{2}{c}^{2}{{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\, {b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{ b}^{2}+{c}^{4}}}t}}{\it \_C2}\,\cos \left ( ct \right ) -4\,{b}^{2}{ {\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}\sqrt {4 \,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}{\it \_C2}\, \cos \left ( ct \right ) -4\,{b}^{2}\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3} +4\,{c}^{2}{b}^{2}+{c}^{4}}{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4 \,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2 }{b}^{2}+{c}^{4}}}t}}{\it \_C1}\,\cos \left ( ct \right ) +4\,{b}^{2}{ {\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}\sqrt {4 \,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}{\it \_C4}\, \cos \left ( ct \right ) +4\,{b}^{2}{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4 \,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\, {c}^{2}{b}^{2}+{c}^{4}}}t}}\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c} ^{2}{b}^{2}+{c}^{4}}{\it \_C3}\,\cos \left ( ct \right ) +4\,\sin \left ( ct \right ) {{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2} -2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+ {c}^{4}}}t}}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4 \,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{\it \_C3}\,{a }^{3}+4\,\cos \left ( ct \right ) {{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\, ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c }^{2}{b}^{2}+{c}^{4}}}t}}\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{ 2}{b}^{2}+{c}^{4}}{\it \_C3}\,{a}^{2}-4\,\cos \left ( ct \right ) \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}{{\rm e}^{-1/ 2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2} {c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C1}\,{a}^{2}+ 4\,\cos \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{ b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b }^{2}+{c}^{4}}}t}}\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{ 2}+{c}^{4}}{\it \_C4}\,{a}^{2}+\sin \left ( ct \right ) {{\rm e}^{-{ \frac {t}{2}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4 \,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}}}} \left ( -4 \,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a {c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}} \right ) ^{{\frac {3}{2}}}{\it \_C3} \,a-4\,\sin \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac- 4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{ 2}{b}^{2}+{c}^{4}}}t}}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2 \,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{ \it \_C4}\,{a}^{3}-\sin \left ( ct \right ) {{\rm e}^{{\frac {t}{2} \sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c} ^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}}}} \left ( -4\,{a}^{2}-4\, ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c }^{2}{b}^{2}+{c}^{4}} \right ) ^{{\frac {3}{2}}}{\it \_C4}\,a+\sin \left ( ct \right ) \left ( -4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\, \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}} \right ) ^{{\frac {3}{2}}}{{\rm e}^{-{\frac {t}{2}\sqrt {-4\,{a}^{2}-4 \,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\, {c}^{2}{b}^{2}+{c}^{4}}}}}}{\it \_C1}\,a-\sin \left ( ct \right ) \left ( -4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c }^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}} \right ) ^{{\frac {3}{2}}} {{\rm e}^{{\frac {t}{2}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}- 2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}}}} {\it \_C2}\,a-4\,\cos \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4\,{a}^ {2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3 }+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4 \,{c}^{2}{b}^{2}+{c}^{4}}{\it \_C2}\,{a}^{2}-4\,\sin \left ( ct \right ) \sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{ a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{{\rm e}^{1/2\, \sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c} ^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C2}\,{a}^{3}-4\, {\it \_C3}\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4 \,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{{\rm e}^{-1/2 \,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{ c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{b}^{2}c\sin \left ( c t \right ) +4\,{\it \_C2}\,{{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{ b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b }^{2}+{c}^{4}}}t}}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\, \sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{b}^{2 }c\sin \left ( ct \right ) -4\,{\it \_C1}\,{{\rm e}^{-1/2\,\sqrt {-4\,{a }^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^ {3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}- 2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{ c}^{4}}}{b}^{2}c\sin \left ( ct \right ) +4\,{b}^{2}\sqrt {-4\,{a}^{2}-4 \,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\, {c}^{2}{b}^{2}+{c}^{4}}}{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b }^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b} ^{2}+{c}^{4}}}t}}{\it \_C1}\,a\sin \left ( ct \right ) -4\,{b}^{2}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4 \,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{{\rm e}^{1/2\,\sqrt {-4\,{a}^{2 }-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+ 4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C2}\,a\sin \left ( ct \right ) +4\, {b}^{2}{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+ 2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}} \sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c} ^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{\it \_C3}\,a\sin \left ( c t \right ) -4\,{b}^{2}{{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2 }-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2} +{c}^{4}}}t}}\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt { 4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{\it \_C4}\,a \sin \left ( ct \right ) +4\,{\it \_C4}\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b} ^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^ {2}+{c}^{4}}}{{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c} ^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4} }}t}}{b}^{2}c\sin \left ( ct \right ) +4\,\sin \left ( ct \right ) \sqrt { -4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4 \,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}{{\rm e}^{-1/2\,\sqrt {-4\,{a}^{ 2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3} +4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C1}\,{a}^{3}-8\,\cos \left ( ct \right ) {{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2 }-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t }}{\it \_C1}\,{a}^{3}c-12\,{c}^{2}\cos \left ( ct \right ) {{\rm e}^{-1/ 2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2} {c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C1}\,{a}^{2}- 4\,{c}^{3}\cos \left ( ct \right ) {{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4 \,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\, {c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C1}\,a-8\,\cos \left ( ct \right ) { {\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C2 }\,{a}^{3}c-12\,{c}^{2}\cos \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4 \,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a {c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C2}\,{a}^{2}-4\,{c}^{3} \cos \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^ {2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{ 2}+{c}^{4}}}t}}{\it \_C2}\,a-8\,\cos \left ( ct \right ) {{\rm e}^{-1/2 \,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{ c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C3}\,{a}^{3}c- 12\,{c}^{2}\cos \left ( ct \right ) {{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4 \,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\, {c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C3}\,{a}^{2}-4\,{c}^{3}\cos \left ( c t \right ) {{\rm e}^{-1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{ 2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}} t}}{\it \_C3}\,a-8\,\cos \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4\,{ a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c} ^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C4}\,{a}^{3}c-12\,{c}^{2} \cos \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^ {2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{ 2}+{c}^{4}}}t}}{\it \_C4}\,{a}^{2}-4\,{c}^{3}\cos \left ( ct \right ) { {\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C4 }\,a-8\,{b}^{2}\cos \left ( ct \right ) {{\rm e}^{-1/2\,\sqrt {-4\,{a}^{ 2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3} +4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C1}\,ac-8\,{b}^{2}\cos \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2} -2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t} }{\it \_C2}\,ac-8\,{b}^{2}\cos \left ( ct \right ) {{\rm e}^{-1/2\, \sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c} ^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C3}\,ac-8\,{b}^{ 2}\cos \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b }^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b} ^{2}+{c}^{4}}}t}}{\it \_C4}\,ac-4\,\cos \left ( ct \right ) \sqrt {4\,{a }^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}{{\rm e}^{-1/2\, \sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c} ^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}{\it \_C1}\,ac-4\,\cos \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}- 2\,{c}^{2}-2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{ c}^{4}}}t}}\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^ {4}}{\it \_C2}\,ac+4\,\cos \left ( ct \right ) {{\rm e}^{-1/2\,\sqrt {-4 \,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2}+2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a {c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t}}\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c} ^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}{\it \_C3}\,ac+4\,\cos \left ( ct \right ) {{\rm e}^{1/2\,\sqrt {-4\,{a}^{2}-4\,ac-4\,{b}^{2}-2\,{c}^{2} +2\,\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}}t} }\sqrt {4\,{a}^{2}{c}^{2}+4\,a{c}^{3}+4\,{c}^{2}{b}^{2}+{c}^{4}}{\it \_C4}\,ac \right ) } \right \} \right \} \]