Internal problem ID [319]
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 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=6 x_{1} \relax (t )-7 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: 0.047 (sec). Leaf size: 35
dsolve([diff(x__1(t),t)=6*x__1(t)-7*x__2(t),diff(x__2(t),t)=x__1(t)-2*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = {\mathrm e}^{-t} c_{1}+7 c_{2} {\mathrm e}^{5 t} \] \[ x_{2} \relax (t ) = {\mathrm e}^{-t} c_{1}+c_{2} {\mathrm e}^{5 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 71
DSolve[{x1'[t]==6*x1[t]-7*x2[t],x2'[t]==x1[t]-2*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{6} e^{-t} \left (7 (c_1-c_2) e^{6 t}-c_1+7 c_2\right ) \\ \text {x2}(t)\to \frac {1}{6} e^{-t} \left ((c_1-c_2) e^{6 t}-c_1+7 c_2\right ) \\ \end{align*}