Internal problem ID [363]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number: problem 6.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )-4 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+9 x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve([diff(x__1(t),t)=1*x__1(t)-4*x__2(t),diff(x__2(t),t)=4*x__1(t)+9*x__2(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{5 t} \left (c_{2} t +c_{1} \right ) \\ x_{2} \left (t \right ) &= -\frac {{\mathrm e}^{5 t} \left (4 c_{2} t +4 c_{1} +c_{2} \right )}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 46
DSolve[{x1'[t]==1*x1[t]-4*x2[t],x2'[t]==4*x1[t]+9*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to -e^{5 t} (c_1 (4 t-1)+4 c_2 t) \\ \text {x2}(t)\to e^{5 t} (4 (c_1+c_2) t+c_2) \\ \end{align*}