Internal problem ID [793]
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: 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=5 x_{1}\relax (t )-x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=3 x_{1}\relax (t )+x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 35
dsolve([diff(x__1(t),t)=5*x__1(t)-1*x__2(t),diff(x__2(t),t)=3*x__1(t)+1*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = c_{1} {\mathrm e}^{4 t}+\frac {c_{2} {\mathrm e}^{2 t}}{3} \] \[ x_{2}\relax (t ) = c_{1} {\mathrm e}^{4 t}+c_{2} {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 55
DSolve[{x1'[t]==5*x1[t]-1*x2[t],x2'[t]==3*x1[t]+1*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{3 t} (c_1 \cosh (t)+(2 c_1-c_2) \sinh (t)) \\ \text {x2}(t)\to e^{3 t} (3 c_1 \sinh (t)+c_2 (\cosh (t)-2 \sinh (t))) \\ \end{align*}