Internal problem ID [806]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 9.1, The Phase Plane: Linear Systems. page 505
Problem number: 15.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-x_{1} \relax (t )-x_{2} \relax (t )-1\\ x_{2}^{\prime }\relax (t )&=2 x_{1} \relax (t )-x_{2} \relax (t )+5 \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 61
dsolve([diff(x__1(t),t)=-1*x__1(t)-1*x__2(t)-1,diff(x__2(t),t)=2*x__1(t)-1*x__2(t)+5],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = -2+\frac {{\mathrm e}^{-t} \sqrt {2}\, \left (c_{2} \cos \left (t \sqrt {2}\right )-c_{1} \sin \left (t \sqrt {2}\right )\right )}{2} \] \[ x_{2} \relax (t ) = 1+{\mathrm e}^{-t} \left (\cos \left (t \sqrt {2}\right ) c_{1}+c_{2} \sin \left (t \sqrt {2}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.175 (sec). Leaf size: 85
DSolve[{x1'[t]==-1*x1[t]-1*x2[t]-1,x2'[t]==2*x1[t]-1*x2[t]+5},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to -2+\frac {1}{2} e^{-t} \left (2 c_1 \cos \left (\sqrt {2} t\right )-\sqrt {2} c_2 \sin \left (\sqrt {2} t\right )\right ) \\ \text {x2}(t)\to 1+e^{-t} \left (c_2 \cos \left (\sqrt {2} t\right )+\sqrt {2} c_1 \sin \left (\sqrt {2} t\right )\right ) \\ \end{align*}