Internal problem ID [321]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.3, The eigenvalue method for linear systems. Page 395
Problem number: problem 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve([diff(x__1(t),t)=-3*x__1(t)+4*x__2(t),diff(x__2(t),t)=6*x__1(t)-5*x__2(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{1} {\mathrm e}^{-9 t}+c_{2} {\mathrm e}^{t} \\ x_{2} \left (t \right ) &= -\frac {3 c_{1} {\mathrm e}^{-9 t}}{2}+c_{2} {\mathrm e}^{t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 74
DSolve[{x1'[t]==-3*x1[t]+4*x2[t],x2'[t]==6*x1[t]-5*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{5} e^{-9 t} \left (c_1 \left (3 e^{10 t}+2\right )+2 c_2 \left (e^{10 t}-1\right )\right ) \\ \text {x2}(t)\to \frac {1}{5} e^{-9 t} \left (3 c_1 \left (e^{10 t}-1\right )+c_2 \left (2 e^{10 t}+3\right )\right ) \\ \end{align*}