73.28.2 problem 39.1 (b)

Internal problem ID [15777]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 39. Critical points, Direction fields and trajectories. Additional Exercises. page 815
Problem number : 39.1 (b)
Date solved : Tuesday, January 28, 2025 at 08:07:01 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=2 x \left (t \right )-5 y \left (t \right )+4\\ \frac {d}{d t}y \left (t \right )&=3 x \left (t \right )-7 y \left (t \right )+5 \end{align*}

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 87

dsolve([diff(x(t),t)=2*x(t)-5*y(t)+4,diff(y(t),t)=3*x(t)-7*y(t)+5],singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{\frac {\left (-5+\sqrt {21}\right ) t}{2}} c_{2} +{\mathrm e}^{-\frac {\left (5+\sqrt {21}\right ) t}{2}} c_{1} +3 \\ y \left (t \right ) &= \frac {{\mathrm e}^{-\frac {\left (5+\sqrt {21}\right ) t}{2}} c_{1} \sqrt {21}}{10}-\frac {{\mathrm e}^{\frac {\left (-5+\sqrt {21}\right ) t}{2}} c_{2} \sqrt {21}}{10}+\frac {9 \,{\mathrm e}^{-\frac {\left (5+\sqrt {21}\right ) t}{2}} c_{1}}{10}+\frac {9 \,{\mathrm e}^{\frac {\left (-5+\sqrt {21}\right ) t}{2}} c_{2}}{10}+2 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.677 (sec). Leaf size: 185

DSolve[{D[x[t],t]==2*x[t]-5*y[t]+4,D[y[t],t]==3*x[t]-7*y[t]+5},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{42} e^{-\frac {1}{2} \left (5+\sqrt {21}\right ) t} \left (126 e^{\frac {1}{2} \left (5+\sqrt {21}\right ) t}+\left (3 \left (7+3 \sqrt {21}\right ) c_1-10 \sqrt {21} c_2\right ) e^{\sqrt {21} t}+\left (21-9 \sqrt {21}\right ) c_1+10 \sqrt {21} c_2\right ) \\ y(t)\to \frac {1}{14} e^{-\frac {1}{2} \left (5+\sqrt {21}\right ) t} \left (28 e^{\frac {1}{2} \left (5+\sqrt {21}\right ) t}+\left (2 \sqrt {21} c_1+\left (7-3 \sqrt {21}\right ) c_2\right ) e^{\sqrt {21} t}-2 \sqrt {21} c_1+\left (7+3 \sqrt {21}\right ) c_2\right ) \\ \end{align*}