Internal problem ID [801]
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: 10.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1} \relax (t )+2 x_{2} \relax (t )\\ x_{2}^{\prime }\relax (t )&=-5 x_{1} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 84
dsolve([diff(x__1(t),t)=1*x__1(t)+2*x__2(t),diff(x__2(t),t)=-5*x__1(t)-0*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = \frac {{\mathrm e}^{\frac {t}{2}} \left (\sqrt {39}\, \sin \left (\frac {\sqrt {39}\, t}{2}\right ) c_{2}-\sqrt {39}\, \cos \left (\frac {\sqrt {39}\, t}{2}\right ) c_{1}-\sin \left (\frac {\sqrt {39}\, t}{2}\right ) c_{1}-\cos \left (\frac {\sqrt {39}\, t}{2}\right ) c_{2}\right )}{10} \] \[ x_{2} \relax (t ) = {\mathrm e}^{\frac {t}{2}} \left (\sin \left (\frac {\sqrt {39}\, t}{2}\right ) c_{1}+\cos \left (\frac {\sqrt {39}\, t}{2}\right ) c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 54
DSolve[{x1'[t]==1*x1[t]+2*x2[t],x2'[t]==-5*x1[t]-1*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to c_1 \cos (3 t)+\frac {1}{3} (c_1+2 c_2) \sin (3 t) \\ \text {x2}(t)\to c_2 \cos (3 t)-\frac {1}{3} (5 c_1+c_2) \sin (3 t) \\ \end{align*}