Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Problem 11
Find the general solution of each of the homogeneous linear systems in Exercises \(1-18\), using the vector-matrix methods of this section, where in each exercise $$\mathbf{x}=\left(\begin{array}{l} x_{1} \\ x_{2} \end{array}\right)$$ $$ \frac{d \mathbf{x}}{d t}=\left(\begin{array}{lr} 1 & -3 \\ 3 & 1 \end{array}\right) \mathbf{x} $$
Problem 11
Use the operator method described in this section to find the general solution of each of the following linear systems. $$ \begin{aligned} &2 \frac{d x}{d t}+\frac{d y}{d t}+x+5 y=4 t \\ &\frac{d x}{d t}+\frac{d y}{d t}+2 x+2 y=2 \end{aligned} $$
Problem 11
Find the general solution of each of the linear systems in Exercises \(1-22\) $$ \begin{aligned} &\frac{d x}{d t}=x-4 y \\ &\frac{d y}{d t}=x+y \end{aligned} $$
Problem 12
Use the operator method described in this section to find the general solution of each of the following linear systems. $$ \begin{aligned} &\frac{d x}{d t}+\frac{d y}{d t}-x+5 y=t^{2} \\ &\frac{d x}{d t}+2 \frac{d y}{d t}-2 x+4 y=2 t+1 \end{aligned} $$
Problem 12
Find the general solution of each of the linear systems in Exercises \(1-22\) $$ \begin{aligned} &\frac{d x}{d t}=2 x-3 y \\ &\frac{d y}{d t}=3 x+2 y \end{aligned} $$
Problem 13
Use the operator method described in this section to find the general solution of each of the following linear systems. $$ \begin{aligned} &2 \frac{d x}{d t}+\frac{d y}{d t}+x+y=t^{2}+4 t \\ &\frac{d x}{d t}+\frac{d y}{d t}+2 x+2 y=2 t^{2}-2 t \end{aligned} $$
Problem 13
Find the general solution of each of the homogeneous linear systems in Exercises \(1-24\), where in each exercise $$\mathbf{x}=\left(\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \end{array}\right)$$ $$ \frac{d \mathbf{x}}{d t}=\left(\begin{array}{rrr} 11 & 6 & 18 \\ 9 & 8 & 18 \\ -9 & -6 & -16 \end{array}\right) \mathbf{x} $$
Problem 13
Find the general solution of each of the linear systems in Exercises \(1-22\) $$ \begin{aligned} &\frac{d x}{d t}=x-3 y \\ &\frac{d y}{d t}=3 x+y \end{aligned} $$
Problem 14
Find the general solution of each of the linear systems in Exercises \(1-22\) $$ \begin{aligned} &\frac{d x}{d t}=5 x-4 y \\ &\frac{d y}{d t}=2 x+y \end{aligned} $$
Problem 14
Use the operator method described in this section to find the general solution of each of the following linear systems. $$ \begin{aligned} &3 \frac{d x}{d t}+2 \frac{d y}{d t}-x+y=t-1 \\ &\frac{d x}{d t}+\frac{d y}{d t}-x=t+2 \end{aligned} $$
