Internal problem ID [320]
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 6.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=9 x_{1}\relax (t )+5 x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=-6 x_{1}\relax (t )-2 x_{2}\relax (t ) \end {align*}
With initial conditions \[ [x_{1}\relax (0) = 1, x_{2}\relax (0) = 0] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve([diff(x__1(t),t) = 9*x__1(t)+5*x__2(t), diff(x__2(t),t) = -6*x__1(t)-2*x__2(t), x__1(0) = 1, x__2(0) = 0],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = 6 \,{\mathrm e}^{4 t}-5 \,{\mathrm e}^{3 t} \] \[ x_{2}\relax (t ) = -6 \,{\mathrm e}^{4 t}+6 \,{\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 33
DSolve[{x1'[t]==9*x1[t]+5*x2[t],x2'[t]==-6*x1[t]-2*x2[t]},{x1[0]==1,x2[0]==0},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{3 t} \left (6 e^t-5\right ) \\ \text {x2}(t)\to -6 e^{3 t} \left (e^t-1\right ) \\ \end{align*}