Internal problem ID [323]
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 9.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-5 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end {align*}
With initial conditions \[ [x_{1} \left (0\right ) = 2, x_{2} \left (0\right ) = 3] \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 34
dsolve([diff(x__1(t),t) = 2*x__1(t)-5*x__2(t), diff(x__2(t),t) = 4*x__1(t)-2*x__2(t), x__1(0) = 2, x__2(0) = 3],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \left (t \right ) = 2 \cos \left (4 t \right )-\frac {11 \sin \left (4 t \right )}{4} \] \[ x_{2} \left (t \right ) = \frac {\sin \left (4 t \right )}{2}+3 \cos \left (4 t \right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 34
DSolve[{x1'[t]==x1[t]-5*x2[t],x2'[t]==x1[t]-x2[t]},{x1[0]==2,x2[0]==3},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to 2 \cos (2 t)-13 \sin (t) \cos (t) \\ \text {x2}(t)\to 3 \cos (2 t)-\sin (t) \cos (t) \\ \end{align*}