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Magazine Problem 32
Find the general solution of the given system. $$ \begin{aligned} &\frac{d x}{d t}=x+y \\ &\frac{d y}{d t}=-2 x-y \end{aligned} $$
Problem 33
Find the general solution of the given system. $$ \begin{aligned} &\frac{d x}{d t}=5 x+y \\ &\frac{d y}{d t}=-2 x+3 y \end{aligned} $$
Problem 34
Find the general solution of the given system. $$ \begin{aligned} &\frac{d x}{d t}=4 x+5 y \\ &\frac{d y}{d t}=-2 x+6 y \end{aligned} $$
Problem 35
Find the general solution of the given system. $$ \mathbf{X}^{\prime}=\left(\begin{array}{ll} 4 & -5 \\ 5 & -4 \end{array}\right) \mathbf{X} $$
Problem 36
Find the general solution of the given system. $$ \mathbf{X}^{\prime}=\left(\begin{array}{ll} 1 & -8 \\ 1 & -3 \end{array}\right) \mathbf{X} $$
Problem 37
Find the general solution of the given system. $$ \begin{aligned} &\frac{d x}{d t}=z \\ &\frac{d y}{d t}=-z \\ &\frac{d z}{d t}=y \end{aligned} $$
Problem 38
Find the general solution of the given system. $$ \begin{aligned} &\frac{d x}{d t}=2 x+y+2 z \\ &\frac{d y}{d t}=3 x+6 z \\ &\frac{d z}{d t}=-4 x-3 z \end{aligned} $$
Problem 39
Find the general solution of the given system. $$ \mathbf{X}^{\prime}=\left(\begin{array}{rrr} 1 & -1 & 2 \\ -1 & 1 & 0 \\ -1 & 0 & 1 \end{array}\right) \mathbf{X} $$
Problem 40
Find the general solution of the given system. $$ \mathbf{X}^{\prime}=\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 6 & 0 \\ -4 & 0 & 4 \end{array}\right) \mathbf{X} $$
Problem 41
Find the general solution of the given system. $$ \mathbf{X}^{\prime}=\left(\begin{array}{rrr} 2 & 5 & 1 \\ -5 & -6 & 4 \\ 0 & 0 & 2 \end{array}\right) \mathbf{X} $$
