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 }\relax (t )&=2 x_{1} \relax (t )-5 x_{2} \relax (t )\\ x_{2}^{\prime }\relax (t )&=x_{1} \relax (t )-2 x_{2} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
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)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = \cos \relax (t ) c_{1}-\sin \relax (t ) c_{2}+2 \sin \relax (t ) c_{1}+2 c_{2} \cos \relax (t ) \] \[ x_{2} \relax (t ) = \sin \relax (t ) c_{1}+c_{2} \cos \relax (t ) \]
✓ Solution by Mathematica
Time used: 0.005 (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*}