Internal problem ID [326]
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 12.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1} \relax (t )-5 x_{2} \relax (t )\\ x_{2}^{\prime }\relax (t )&=x_{1} \relax (t )+3 x_{2} \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 60
dsolve([diff(x__1(t),t)=x__1(t)-5*x__2(t),diff(x__2(t),t)=x__1(t)+3*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = {\mathrm e}^{2 t} \left (2 c_{1} \cos \left (2 t \right )-c_{2} \cos \left (2 t \right )-c_{1} \sin \left (2 t \right )-2 c_{2} \sin \left (2 t \right )\right ) \] \[ x_{2} \relax (t ) = {\mathrm e}^{2 t} \left (c_{1} \sin \left (2 t \right )+c_{2} \cos \left (2 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 67
DSolve[{x1'[t]==x1[t]-5*x2[t],x2'[t]==x1[t]+3*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{2} e^{2 t} (2 c_1 \cos (2 t)-(c_1+5 c_2) \sin (2 t)) \\ \text {x2}(t)\to \frac {1}{2} e^{2 t} (2 c_2 \cos (2 t)+(c_1+c_2) \sin (2 t)) \\ \end{align*}