Internal problem ID [11576]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 4, Linear Systems. Exercises page 244
Problem number: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=-5 x+3 y \left (t \right )+{\mathrm e}^{-t}\\ y^{\prime }\left (t \right )&=2 x-10 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 48
dsolve([diff(x(t),t)=-5*x(t)+3*y(t)+exp(-t),diff(y(t),t)=2*x(t)-10*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -\frac {{\mathrm e}^{-11 t} c_{2}}{2}+3 \,{\mathrm e}^{-4 t} c_{1} +\frac {3 \,{\mathrm e}^{-t}}{10} \] \[ y \left (t \right ) = {\mathrm e}^{-11 t} c_{2} +{\mathrm e}^{-4 t} c_{1} +\frac {{\mathrm e}^{-t}}{15} \]
✓ Solution by Mathematica
Time used: 0.092 (sec). Leaf size: 88
DSolve[{x'[t]==-5*x[t]+3*y[t]+Exp[-t],y'[t]==2*x[t]-10*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{70} e^{-11 t} \left (21 e^{10 t}+30 (2 c_1+c_2) e^{7 t}+10 (c_1-3 c_2)\right ) y(t)\to \frac {1}{105} e^{-11 t} \left (7 e^{10 t}+15 (2 c_1+c_2) e^{7 t}-30 (c_1-3 c_2)\right ) \end{align*}