73.27.2 problem 38.2

Internal problem ID [15758]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 38. Systems of differential equations. A starting point. Additional Exercises. page 786
Problem number : 38.2
Date solved : Tuesday, January 28, 2025 at 08:06:44 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=4 x \left (t \right )-3 y \left (t \right )\\ \frac {d}{d t}y \left (t \right )&=6 x \left (t \right )-7 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 35

dsolve([diff(x(t),t)=4*x(t)-3*y(t),diff(y(t),t)=6*x(t)-7*y(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 74

DSolve[{D[x[t],t]==4*x[t]-3*y[t],D[y[t],t]==6*x[t]-7*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{7} e^{-5 t} \left (c_1 \left (9 e^{7 t}-2\right )-3 c_2 \left (e^{7 t}-1\right )\right ) \\ y(t)\to \frac {1}{7} e^{-5 t} \left (6 c_1 \left (e^{7 t}-1\right )+c_2 \left (9-2 e^{7 t}\right )\right ) \\ \end{align*}