Internal problem ID [14040]
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 (a).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )-5 y \left (t \right )\\ y^{\prime }\left (t \right )&=3 x \left (t \right )-7 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 86
dsolve([diff(x(t),t)=2*x(t)-5*y(t),diff(y(t),t)=3*x(t)-7*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{\frac {\left (-5+\sqrt {21}\right ) t}{2}}+c_{2} {\mathrm e}^{-\frac {\left (5+\sqrt {21}\right ) t}{2}} \\ y \left (t \right ) &= \frac {c_{2} {\mathrm e}^{-\frac {\left (5+\sqrt {21}\right ) t}{2}} \sqrt {21}}{10}-\frac {c_{1} {\mathrm e}^{\frac {\left (-5+\sqrt {21}\right ) t}{2}} \sqrt {21}}{10}+\frac {9 c_{2} {\mathrm e}^{-\frac {\left (5+\sqrt {21}\right ) t}{2}}}{10}+\frac {9 c_{1} {\mathrm e}^{\frac {\left (-5+\sqrt {21}\right ) t}{2}}}{10} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 150
DSolve[{x'[t]==2*x[t]-5*y[t],y'[t]==3*x[t]-7*y[t]},{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 (3 c_1 \left (\left (7+3 \sqrt {21}\right ) e^{\sqrt {21} t}+7-3 \sqrt {21}\right )-10 \sqrt {21} c_2 \left (e^{\sqrt {21} t}-1\right )\right ) \\ y(t)\to \frac {1}{14} e^{-\frac {1}{2} \left (5+\sqrt {21}\right ) t} \left (2 \sqrt {21} c_1 \left (e^{\sqrt {21} t}-1\right )-c_2 \left (\left (3 \sqrt {21}-7\right ) e^{\sqrt {21} t}-7-3 \sqrt {21}\right )\right ) \\ \end{align*}