Chapter 6.5, Problem 13E

(a)

To determine

The solution of the system of differential equations $x^{\prime }=x-6y+f_1\left(t\right)$ and $y^{\prime }=x-4y+f_2\left(t\right)$ where $f_1\left(t\right)=0$, $f_2\left(t\right)=0$.

(b)

To determine

The solution of the system of differential equation $x^{\prime }=x-6y+f_1\left(t\right)$ and $y^{\prime }=x-4y+f_2\left(t\right)$, where $f_1\left(t\right)=0$, $f_2\left(t\right)=-2e^t$.

(c)

To determine

The solution of the system of differential equation $x^{\prime }=x-6y+f_1\left(t\right)$ and $y^{\prime }=x-4y+f_2\left(t\right)$ with boundary condition $f_1\left(t\right)=0$, $f_2\left(t\right)=-2e^t$.