Internal problem ID [317]
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 3.
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 )&=3 x_{1}\relax (t )+2 x_{2}\relax (t ) \end {align*}
With initial conditions \[ [x_{1}\relax (0) = 1, x_{2}\relax (0) = 1] \]
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 34
dsolve([diff(x__1(t),t) = 3*x__1(t)+4*x__2(t), diff(x__2(t),t) = 3*x__1(t)+2*x__2(t), x__1(0) = 1, x__2(0) = 1],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = -\frac {{\mathrm e}^{-t}}{7}+\frac {8 \,{\mathrm e}^{6 t}}{7} \] \[ x_{2}\relax (t ) = \frac {{\mathrm e}^{-t}}{7}+\frac {6 \,{\mathrm e}^{6 t}}{7} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 44
DSolve[{x1'[t]==3*x1[t]+4*x2[t],x2'[t]==3*x1[t]+2*x2[t]},{x1[0]==1,x2[0]==1},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{7} e^{-t} \left (8 e^{7 t}-1\right ) \\ \text {x2}(t)\to \frac {1}{7} e^{-t} \left (6 e^{7 t}+1\right ) \\ \end{align*}