演習問題

1.

次の連立微分方程式を解け．

(a)

$${ \left\{\begin{array}{rc} x_{1}^{\prime} =& 6x_{1} + 8x_{2}\\ x_{2}^{\prime} =& -x_{1} + 2x_{2} \end{array} \right .}$$

(b)

$${ \left\{\begin{array}{rc} x_{1}^{\prime} =& 2x_{1} - x_{2}\\ x_{2}^{\prime} =& 4x_{1} + 6x_{2} \end{array} \right . }$$

(c)

$${ \left\{\begin{array}{rc} x_{1}^{\prime} =& 5x_{1} + 2x_{2} + 2x_... ...2} - 4x_{3}\\ x_{3}^{\prime} =& 2x_{1} - 4x_{2} + 2x_{3} \end{array} \right .}$$

(d)

$${ {\bf X}^{\prime} = \left(\begin{array}{ccc} 1&0&1\\ 1&1&0\\ -2&0&-1 \end{array}\right){\bf X} }$$

(e)

$${ \left\{\begin{array}{rc} 4x_{1}^{\prime} + x_{1} + 2x_{2}^{\prim... ...\\ x_{1}^{\prime} - x_{1} + x_{2}^{\prime} + x_{2} =& 0 \end{array} \right . }$$

(f)

$${ \left\{\begin{array}{rc} x_{1}^{\prime} + x_{1} + 2x_{2}^{\prime... ...2} =& 0\\ x_{1}^{\prime} - 2x_{1} + 5x_{2}^{\prime} =& 0 \end{array} \right .}$$