Internal problem ID [325]
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 11.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1} \relax (t )-2 x_{2} \relax (t )\\ x_{2}^{\prime }\relax (t )&=2 x_{1} \relax (t )+x_{2} \relax (t ) \end {align*}
With initial conditions \[ [x_{1} \relax (0) = 0, x_{2} \relax (0) = 4] \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 24
dsolve([diff(x__1(t),t) = x__1(t)-2*x__2(t), diff(x__2(t),t) = 2*x__1(t)+x__2(t), x__1(0) = 0, x__2(0) = 4],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = -4 \,{\mathrm e}^{t} \sin \left (2 t \right ) \] \[ x_{2} \relax (t ) = 4 \,{\mathrm e}^{t} \cos \left (2 t \right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 26
DSolve[{x1'[t]==x1[t]-2*x2[t],x2'[t]==2*x1[t]+x2[t]},{x1[0]==0,x2[0]==4},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to -4 e^t \sin (2 t) \\ \text {x2}(t)\to 4 e^t \cos (2 t) \\ \end{align*}