Internal problem ID [316]
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 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=2 x_{1}\relax (t )+3 x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=2 x_{1}\relax (t )+x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 36
dsolve([diff(x__1(t),t)=2*x__1(t)+3*x__2(t),diff(x__2(t),t)=2*x__1(t)+x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = -{\mathrm e}^{-t} c_{1}+\frac {3 c_{2} {\mathrm e}^{4 t}}{2} \] \[ x_{2}\relax (t ) = {\mathrm e}^{-t} c_{1}+c_{2} {\mathrm e}^{4 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 68
DSolve[{x1'[t]==2*x1[t]+3*x2[t],x2'[t]==2*x1[t]+x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{5} e^{-t} \left (3 (c_1+c_2) e^{5 t}+2 c_1-3 c_2\right ) \\ \text {x2}(t)\to \frac {1}{5} e^{-t} \left (2 (c_1+c_2) e^{5 t}-2 c_1+3 c_2\right ) \\ \end{align*}