Internal problem ID [14022]
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.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=4 x \left (t \right )-3 y \left (t \right )\\ y^{\prime }\left (t \right )&=6 x \left (t \right )-7 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
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 ) &= c_{1} {\mathrm e}^{-5 t}+c_{2} {\mathrm e}^{2 t} \\ y \left (t \right ) &= 3 c_{1} {\mathrm e}^{-5 t}+\frac {2 c_{2} {\mathrm e}^{2 t}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 74
DSolve[{x'[t]==4*x[t]-3*y[t],y'[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*}