Internal problem ID [318]
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 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=4 x_{1}\relax (t )+x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=6 x_{1}\relax (t )-x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 35
dsolve([diff(x__1(t),t)=4*x__1(t)+x__2(t),diff(x__2(t),t)=6*x__1(t)-x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = -\frac {c_{1} {\mathrm e}^{-2 t}}{6}+c_{2} {\mathrm e}^{5 t} \] \[ x_{2}\relax (t ) = c_{1} {\mathrm e}^{-2 t}+c_{2} {\mathrm e}^{5 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 68
DSolve[{x1'[t]==4*x1[t]+x2[t],x2'[t]==6*x1[t]-x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{7} e^{-2 t} \left ((6 c_1+c_2) e^{7 t}+c_1-c_2\right ) \\ \text {x2}(t)\to \frac {1}{7} e^{-2 t} \left (6 c_1 \left (e^{7 t}-1\right )+c_2 \left (e^{7 t}+6\right )\right ) \\ \end{align*}