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 }\relax (t )&=x_{1} \relax (t )-4 x_{2} \relax (t )\\ x_{2}^{\prime }\relax (t )&=4 x_{1} \relax (t )+9 x_{2} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 35
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)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = -\frac {{\mathrm e}^{5 t} \left (4 t c_{2}+4 c_{1}-c_{2}\right )}{4} \] \[ x_{2} \relax (t ) = {\mathrm e}^{5 t} \left (t c_{2}+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 44
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} (-4 c_1 t-4 c_2 t+c_1) \\ \text {x2}(t)\to e^{5 t} (4 (c_1+c_2) t+c_2) \\ \end{align*}