91Ó°ÊÓ

Write the given linear system in matrix form. $$\begin{aligned} &\frac{d x}{d t}=3 x-5 y\\\ &\frac{d y}{d t}=4 x+8 y \end{aligned}$$

Use the method of undetermined coefficients to solve the given non-homogeneous system. $$\begin{aligned} &\frac{d x}{d t}=2 x+3 y-7\\\ &\frac{d y}{d t}=-x-2 y+5 \end{aligned}$$

Find the general solution of the given system. $$\begin{aligned} &\frac{d x}{d t}=x+2 y\\\ &\frac{d y}{d t}=4 x+3 y \end{aligned}$$

Use the method of undetermined coefficients to solve the given non-homogeneous system. $$\begin{aligned} &\frac{d x}{d t}=5 x+9 y+2\\\ &\frac{d y}{d t}=-x+11 y+6 \end{aligned}$$

Write the given linear system in matrix form. $$\begin{aligned} &\frac{d x}{d t}=4 x-7 y\\\ &\frac{d y}{d t}=5 x \end{aligned}$$

Find the general solution of the given system. $$\begin{aligned} &\frac{d x}{d t}=2 x+2 y\\\ &\frac{d y}{d t}=x+3 y \end{aligned}$$

Find the general solution of the given system. $$\begin{aligned} &\frac{d x}{d t}=-4 x+2 y\\\ &\frac{d y}{d t}=-\frac{5}{2} x+2 y \end{aligned}$$

Write the given linear system in matrix form. $$\begin{aligned} &\frac{d x}{d t}=-3 x+4 y-9 z\\\ &\frac{d y}{d t}=6 x-y\\\ &\frac{d z}{d t}=10 x+4 y+3 z \end{aligned}$$

Use the method of undetermined coefficients to solve the given non-homogeneous system. $$\mathbf{X}^{\prime}=\left(\begin{array}{ll} 1 & 3 \\ 3 & 1 \end{array}\right) \mathbf{X}+\left(\begin{array}{l} -2 t^{2} \\ t+5 \end{array}\right)$$

Write the given linear system in matrix form. $$\begin{aligned} &\frac{d x}{d t}=x-y\\\ &\frac{d y}{d t}=x+2 z\\\ &\frac{d z}{d t}=-x+z \end{aligned}$$