Internal problem ID [797]
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: 6.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-5 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 38
dsolve([diff(x__1(t),t)=2*x__1(t)-5*x__2(t),diff(x__2(t),t)=1*x__1(t)-2*x__2(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right ) \\ x_{2} \left (t \right ) &= -\frac {c_{1} \cos \left (t \right )}{5}+\frac {c_{2} \sin \left (t \right )}{5}+\frac {2 c_{1} \sin \left (t \right )}{5}+\frac {2 c_{2} \cos \left (t \right )}{5} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 41
DSolve[{x1'[t]==2*x1[t]-5*x2[t],x2'[t]==1*x1[t]-2*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to c_1 (2 \sin (t)+\cos (t))-5 c_2 \sin (t) \\ \text {x2}(t)\to c_2 \cos (t)+(c_1-2 c_2) \sin (t) \\ \end{align*}