常微分方程式
. , n . ) {\displaystyle {\boldsymbol {F}}(t,{\boldsymbol {x}}(t),{\boldsymbol {x}}^{(1)}(t),\dots ,{\boldsymbol {x}}^{(n)}(t))={\boldsymbol {0}}\quad \left({\boldsymbol {x}}^{(k)}(t):={\frac {\mathrm {d} ^{k}}{\mathrm {d} t^{k}}}{\boldsymbol {x}}(t),\,\mathrm {for} ~\,k=0,1,\dots ,n.\right)}
ここで F, x は
F ( t , x ( t ) , x ( 1 ) ( t ) , ... , x ( n ) ( t ) ) = ( F 1 ( t , x ( t ) , x ( 1 ) ( t ) , ... , x ( n ) ( t ) ) , ... , F r ( t , x ( t ) , x ( 1 ) ( t ) , ... , x ( n ) ( t ) ) ) x ( t ) = ( x 1 ( t ) , ...