Internal problem ID [12857]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 10. Applications of Systems of Equations. Exercises 10.2 page 432
Problem number: 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 x \left (t \right )+3 y \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right )+2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve([diff(x(t),t)=-2*x(t)+3*y(t),diff(y(t),t)=-x(t)+2*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-t} \\ y \left (t \right ) &= c_{1} {\mathrm e}^{t}+\frac {c_{2} {\mathrm e}^{-t}}{3} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 72
DSolve[{x'[t]==-2*x[t]+3*y[t],y'[t]==-x[t]+2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^{-t} \left (3 c_2 \left (e^{2 t}-1\right )-c_1 \left (e^{2 t}-3\right )\right ) \\ y(t)\to -\frac {1}{2} e^{-t} \left (c_1 \left (e^{2 t}-1\right )+c_2 \left (1-3 e^{2 t}\right )\right ) \\ \end{align*}