Internal problem ID [12863]
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: 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-5 x \left (t \right )-y \left (t \right )+2\\ y^{\prime }\left (t \right )&=3 x \left (t \right )-y \left (t \right )-3 \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 39
dsolve([diff(x(t),t)=-5*x(t)-y(t)+2,diff(y(t),t)=3*x(t)-1*y(t)-3],singsol=all)
\begin{align*} x \left (t \right ) &= \frac {5}{8}-\frac {{\mathrm e}^{-4 t} c_{1}}{2}+c_{2} {\mathrm e}^{-2 t} \\ y \left (t \right ) &= \frac {{\mathrm e}^{-4 t} c_{1}}{2}-3 c_{2} {\mathrm e}^{-2 t}-\frac {9}{8} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 93
DSolve[{x'[t]==-5*x[t]-y[t]+2,y'[t]==3*x[t]-1*y[t]-3},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{48} e^{-4 t} \left (30 e^{4 t}-(1+24 c_1+24 c_2) e^{2 t}+3+72 c_1+24 c_2\right ) \\ y(t)\to \frac {1}{16} e^{-4 t} \left (-18 e^{4 t}+(1+24 c_1+24 c_2) e^{2 t}-1-24 c_1-8 c_2\right ) \\ \end{align*}