Internal problem ID [359]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=3 x_{1}\relax (t )-x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=x_{1}\relax (t )+x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 29
dsolve([diff(x__1(t),t)=3*x__1(t)-1*x__2(t),diff(x__2(t),t)=1*x__1(t)+1*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = {\mathrm e}^{2 t} \left (c_{2} t +c_{1}+c_{2}\right ) \] \[ x_{2}\relax (t ) = {\mathrm e}^{2 t} \left (c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 44
DSolve[{x1'[t]==3*x1[t]-1*x2[t],x2'[t]==1*x1[t]+1*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{2 t} (c_1 (t+1)-c_2 t) \\ \text {x2}(t)\to e^{2 t} ((c_1-c_2) t+c_2) \\ \end{align*}