Internal problem ID [14042]
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 (c).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )+y \left (t \right )\\ y^{\prime }\left (t \right )&=6 x \left (t \right )+2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve([diff(x(t),t)=3*x(t)+y(t),diff(y(t),t)=6*x(t)+2*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} +c_{2} {\mathrm e}^{5 t} \\ y \left (t \right ) &= 2 c_{2} {\mathrm e}^{5 t}-3 c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 63
DSolve[{x'[t]==3*x[t]+y[t],y'[t]==6*x[t]+2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{5} \left (c_1 \left (3 e^{5 t}+2\right )+c_2 \left (e^{5 t}-1\right )\right ) \\ y(t)\to \frac {1}{5} \left (6 c_1 \left (e^{5 t}-1\right )+c_2 \left (2 e^{5 t}+3\right )\right ) \\ \end{align*}