55.1.16 problem Example 8.3.4 from Handout chapter 8.2

Internal problem ID [8712]
Book : Selected problems from homeworks from different courses
Section : Math 2520, summer 2021. Differential Equations and Linear Algebra. Normandale college, Bloomington, Minnesota
Problem number : Example 8.3.4 from Handout chapter 8.2
Date solved : Monday, January 27, 2025 at 04:20:03 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=6 x \left (t \right )-7 y \left (t \right )+10\\ \frac {d}{d t}y \left (t \right )&=x \left (t \right )-2 y \left (t \right )-2 \,{\mathrm e}^{t} \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 44

dsolve([diff(x(t),t)=6*x(t)-7*y(t)+10,diff(y(t),t)=x(t)-2*y(t)-2*exp(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{-t}+{\mathrm e}^{5 t} c_{1} -\frac {7 \,{\mathrm e}^{t}}{4}-4 \\ y \left (t \right ) &= c_{2} {\mathrm e}^{-t}+\frac {{\mathrm e}^{5 t} c_{1}}{7}-\frac {5 \,{\mathrm e}^{t}}{4}-2 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.089 (sec). Leaf size: 90

DSolve[{D[x[t],t]==6*x[t]-7*y[t]+10,D[y[t],t]==x[t]-2*y[t]-2*Exp[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to -\frac {7 e^t}{4}-\frac {1}{6} (c_1-7 c_2) e^{-t}+\frac {7}{6} (c_1-c_2) e^{5 t}-4 \\ y(t)\to -\frac {5 e^t}{4}-\frac {1}{6} (c_1-7 c_2) e^{-t}+\frac {1}{6} (c_1-c_2) e^{5 t}-2 \\ \end{align*}