Internal problem ID [12243]
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: 2.2 (iii).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right )-3 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve([diff(x(t),t)=x(t),diff(y(t),t)=2*x(t)-3*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = 2 c_{2} {\mathrm e}^{t} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{-3 t}+c_{2} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 38
DSolve[{x'[t]==x[t],y'[t]==2*x[t]-3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^t y(t)\to \frac {1}{2} e^{-3 t} \left (c_1 \left (e^{4 t}-1\right )+2 c_2\right ) \end{align*}