Internal problem ID [362]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=7 x_{1} \left (t \right )+x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=-4 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 33
dsolve([diff(x__1(t),t)=7*x__1(t)+1*x__2(t),diff(x__2(t),t)=-4*x__1(t)+3*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \left (t \right ) = -\frac {{\mathrm e}^{5 t} \left (2 c_{2} t +2 c_{1} +c_{2} \right )}{4} \] \[ x_{2} \left (t \right ) = {\mathrm e}^{5 t} \left (c_{2} t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 45
DSolve[{x1'[t]==7*x1[t]+1*x2[t],x2'[t]==-4*x1[t]+3*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{5 t} (2 c_1 t+c_2 t+c_1) \\ \text {x2}(t)\to e^{5 t} (c_2-2 (2 c_1+c_2) t) \\ \end{align*}