Internal problem ID [12559]
Book: Nonlinear Ordinary Differential Equations by D.W.Jordna and P.Smith. 4th edition 1999.
Oxford Univ. Press. NY
Section: Chapter 2. Plane autonomous systems and linearization. Problems page 79
Problem number: 2.1 (v).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=4 x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=3 x \left (t \right )-y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 31
dsolve([diff(x(t),t)=4*x(t)-2*y(t),diff(y(t),t)=3*x(t)-y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{2 t} \\ y \left (t \right ) &= \frac {3 c_{1} {\mathrm e}^{t}}{2}+c_{2} {\mathrm e}^{2 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 56
DSolve[{x'[t]==4*x[t]-2*y[t],y'[t]==3*x[t]-y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t \left (c_1 \left (3 e^t-2\right )-2 c_2 \left (e^t-1\right )\right ) \\ y(t)\to e^t \left (3 c_1 \left (e^t-1\right )+c_2 \left (3-2 e^t\right )\right ) \\ \end{align*}