Internal problem ID [360]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1} \relax (t )-2 x_{2} \relax (t )\\ x_{2}^{\prime }\relax (t )&=2 x_{1} \relax (t )+5 x_{2} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 35
dsolve([diff(x__1(t),t)=1*x__1(t)-2*x__2(t),diff(x__2(t),t)=2*x__1(t)+5*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = -\frac {{\mathrm e}^{3 t} \left (2 t c_{2}+2 c_{1}-c_{2}\right )}{2} \] \[ x_{2} \relax (t ) = {\mathrm e}^{3 t} \left (t c_{2}+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 44
DSolve[{x1'[t]==1*x1[t]-2*x2[t],x2'[t]==2*x1[t]+5*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{3 t} (-2 c_1 t-2 c_2 t+c_1) \\ \text {x2}(t)\to e^{3 t} (2 (c_1+c_2) t+c_2) \\ \end{align*}