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 }\relax (t )&=-3 x_{1} \relax (t )+4 x_{2} \relax (t )\\ x_{2}^{\prime }\relax (t )&=6 x_{1} \relax (t )-5 x_{2} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (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)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = c_{1} {\mathrm e}^{t}-\frac {2 c_{2} {\mathrm e}^{-9 t}}{3} \] \[ x_{2} \relax (t ) = c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-9 t} \]
✓ 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 {2}{5} (c_1-c_2) e^{-9 t}+\frac {1}{5} (3 c_1+2 c_2) e^t \\ \text {x2}(t)\to \frac {1}{5} e^{-9 t} \left ((3 c_1+2 c_2) e^{10 t}-3 c_1+3 c_2\right ) \\ \end{align*}