演習問題


1.
次の連立微分方程式を解け.
(a)
$\displaystyle{ \left\{\begin{array}{rc}
x_{1}^{\prime} =& x_{1} + 4x_{2}\\
x_{2}^{\prime} =& x_{1} + x_{2}
\end{array} \right .}$
(b)
$\displaystyle{ \left\{\begin{array}{rc}
x_{1}^{\prime} =& 6x_{1} - 3x_{2}\\
x_{2}^{\prime} =& 2x_{1} + x_{2}
\end{array} \right . }$
(c)
$\displaystyle{ \left\{\begin{array}{rc}
x_{1}^{\prime} =& x_{1} + x_{2} - x_{3}...
...{2}^{\prime} =& 2x_{2}\\
x_{3}^{\prime} =& x_{2} - x_{3}
\end{array} \right .}$
(d)
$\displaystyle{ {\bf X}^{\prime} = \left(\begin{array}{ccc}
1&-3&2\\
0&-1&0\\
0&-1&-2
\end{array}\right){\bf X} }$
(e)
$\displaystyle{ \left\{\begin{array}{rc}
x_{1}^{\prime} + x_{2}^{\prime} + 2x_{2} =& 0\\
x_{1}^{\prime} - 3x_{1} - 2x_{2} =& 0
\end{array} \right . }$
(f)
$\displaystyle{ \left\{\begin{array}{rc}
x_{1}^{\prime} + 6x_{1} + x_{2}^{\prime...
...{2} =& 0\\
x_{1}^{\prime} - x_{2}^{\prime} + x_{2} =& 0
\end{array} \right . }$