\[ \boxed { \left \{ {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) =h \left ( t \right ) y \left ( t \right ) -g \left ( t \right ) z \left ( t \right ) ,{\frac {\rm d}{{\rm d}t}}y \left ( t \right ) =f \left ( t \right ) z \left ( t \right ) -h \left ( t \right ) x \left ( t \right ) ,{\frac {\rm d}{{\rm d}t}}z \left ( t \right ) =x \left ( t \right ) g \left ( t \right ) -y \left ( t \right ) f \left ( t \right ) \right \} } \]
Mathematica: cpu = 0.006501 (sec), leaf count = 61 \[ \text {DSolve}\left [\left \{x'(t)=h(t) y(t)-g(t) z(t),y'(t)=f(t) z(t)-h(t) x(t),z'(t)=g(t) x(t)-f(t) y(t)\right \},\{x(t),y(t),z(t)\},t\right ] \]
Maple: cpu = 0.530 (sec), leaf count = 2014 \[ \left \{ \left \{ x \left ( t \right ) ={\it DESol} \left ( \left \{ { \frac {{\rm d}^{3}}{{\rm d}{t}^{3}}}{\it \_Y} \left ( t \right ) + \left ( {\frac { \left ( {\frac {\rm d}{{\rm d}t}}f \left ( t \right ) \right ) \left ( g \left ( t \right ) \right ) ^{2}}{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{ {\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}+{\frac { \left ( h \left ( t \right ) \right ) ^{2}{\frac {\rm d}{{\rm d}t}}f \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+ h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}+{\frac { \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}h \left ( t \right ) \right ) g \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{ {\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-{\frac {h \left ( t \right ) {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}g \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) { \frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{ {\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}+2\,{\frac { \left ( {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) \right ) f \left ( t \right ) g \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}+2\,{\frac {h \left ( t \right ) \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) f \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+ h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }} \right ) {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}{\it \_Y} \left ( t \right ) + \left ( -{\frac { \left ( f \left ( t \right ) \right ) ^{3} \left ( g \left ( t \right ) \right ) ^{2}}{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t} }h \left ( t \right ) \right ) g \left ( t \right ) }}-{\frac { \left ( h \left ( t \right ) \right ) ^{2} \left ( f \left ( t \right ) \right ) ^{3 }}{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-{ \frac {f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{4}}{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) { \frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{ {\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-{\frac { \left ( h \left ( t \right ) \right ) ^{4}f \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) { \frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{ {\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}+{\frac { \left ( h \left ( t \right ) \right ) ^{3}{\frac {\rm d}{{\rm d}t}}g \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2} +h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-{\frac { \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) \left ( g \left ( t \right ) \right ) ^{3}}{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t} }h \left ( t \right ) \right ) g \left ( t \right ) }}-2\,{\frac {f \left ( t \right ) \left ( {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) \right ) ^{2}}{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+ h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-2\,{\frac { \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) ^{2}f \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{ {\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-{\frac { \left ( { \frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}h \left ( t \right ) \right ) { \frac {\rm d}{{\rm d}t}}g \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{ {\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}+{\frac { \left ( { \frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}g \left ( t \right ) \right ) { \frac {\rm d}{{\rm d}t}}h \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{ {\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-2\,{\frac { \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}}{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}+3\,{\frac {h \left ( t \right ) \left ( f \left ( t \right ) \right ) ^{2}{\frac {\rm d}{{\rm d}t}}g \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+ h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-3\,{\frac { \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) \left ( f \left ( t \right ) \right ) ^{2}g \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+ h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}+{\frac {h \left ( t \right ) \left ( {\frac {\rm d}{{\rm d} t}}g \left ( t \right ) \right ) \left ( g \left ( t \right ) \right ) ^{2 }}{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-{ \frac { \left ( h \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{ {\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t} }h \left ( t \right ) \right ) g \left ( t \right ) }}+{\frac {f \left ( t \right ) g \left ( t \right ) {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}g \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2} +h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}+{\frac {h \left ( t \right ) \left ( {\frac {{\rm d}^{2}}{ {\rm d}{t}^{2}}}h \left ( t \right ) \right ) f \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) { \frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{ {\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-{\frac { \left ( {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) \right ) g \left ( t \right ) {\frac {\rm d}{{\rm d}t}}f \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t} }h \left ( t \right ) \right ) g \left ( t \right ) }}-{\frac {h \left ( t \right ) \left ( {\frac {\rm d}{{\rm d}t}}f \left ( t \right ) \right ) {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{ {\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }} \right ) {\frac {\rm d}{{\rm d}t}}{\it \_Y} \left ( t \right ) + \left ( {\frac { \left ( g \left ( t \right ) \right ) ^{4}{\frac {\rm d}{{\rm d}t}}f \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+ h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}+{\frac { \left ( h \left ( t \right ) \right ) ^{4}{\frac {\rm d}{{\rm d}t}}f \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}+{\frac { \left ( {\frac { {\rm d}^{2}}{{\rm d}{t}^{2}}}h \left ( t \right ) \right ) \left ( g \left ( t \right ) \right ) ^{3}}{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-{\frac { \left ( h \left ( t \right ) \right ) ^{3}{\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}g \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-{ \frac { \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) \left ( {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) \right ) g \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+ h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-{\frac {h \left ( t \right ) \left ( {\frac {\rm d}{{\rm d} t}}h \left ( t \right ) \right ) f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}}{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-{\frac { \left ( {\frac {\rm d}{{\rm d}t }}g \left ( t \right ) \right ) f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{3}}{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-{\frac { \left ( h \left ( t \right ) \right ) ^{3} \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) f \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2 }f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}+2\,{\frac { \left ( h \left ( t \right ) \right ) ^{2} \left ( g \left ( t \right ) \right ) ^{2}{\frac {\rm d}{ {\rm d}t}}f \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{ 2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}+3\,{\frac {h \left ( t \right ) \left ( { \frac {\rm d}{{\rm d}t}}g \left ( t \right ) \right ) ^{2}g \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+ h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-3\,{\frac { \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) \left ( {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) \right ) \left ( g \left ( t \right ) \right ) ^{2}}{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{ {\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}+3\,{\frac { \left ( h \left ( t \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+ h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-{\frac {h \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}{\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}g \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}+{ \frac { \left ( h \left ( t \right ) \right ) ^{2} \left ( {\frac {{\rm d} ^{2}}{{\rm d}{t}^{2}}}h \left ( t \right ) \right ) g \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }}-3 \,{\frac {h \left ( t \right ) \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) ^{2}g \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) {\frac {\rm d}{ {\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }} \right ) {\it \_Y} \left ( t \right ) \right \} , \left \{ {\it \_Y} \left ( t \right ) \right \} \right ) ,y \left ( t \right ) ={\frac {- \left ( h \left ( t \right ) \right ) ^{2}x \left ( t \right ) g \left ( t \right ) -x \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{3}-h \left ( t \right ) \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) f \left ( t \right ) - \left ( {\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}x \left ( t \right ) \right ) g \left ( t \right ) + \left ( {\frac {\rm d}{{\rm d}t} }g \left ( t \right ) \right ) {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+ h \left ( t \right ) {\frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }},z \left ( t \right ) ={\frac {- \left ( h \left ( t \right ) \right ) ^{3}x \left ( t \right ) -h \left ( t \right ) x \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+ \left ( {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) \right ) g \left ( t \right ) f \left ( t \right ) -h \left ( t \right ) {\frac {{\rm d}^{2}}{{\rm d}{t}^ {2}}}x \left ( t \right ) + \left ( {\frac {\rm d}{{\rm d}t}}h \left ( t \right ) \right ) {\frac {\rm d}{{\rm d}t}}x \left ( t \right ) }{- \left ( h \left ( t \right ) \right ) ^{2}f \left ( t \right ) -f \left ( t \right ) \left ( g \left ( t \right ) \right ) ^{2}+h \left ( t \right ) { \frac {\rm d}{{\rm d}t}}g \left ( t \right ) - \left ( {\frac {\rm d}{ {\rm d}t}}h \left ( t \right ) \right ) g \left ( t \right ) }} \right \} \right \} \]