Internal problem ID [1831]
Book: Differential equations and their applications, 4th ed., M. Braun
Section: Section 3.8, Systems of differential equations. The eigenva1ue-eigenvector method. Page
339
Problem number: 8.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1} \relax (t )-3 x_{2} \relax (t )\\ x_{2}^{\prime }\relax (t )&=-2 x_{1} \relax (t )+2 x_{2} \relax (t ) \end {align*}
With initial conditions \[ [x_{1} \relax (0) = 0, x_{2} \relax (0) = 5] \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 34
dsolve([diff(x__1(t),t) = x__1(t)-3*x__2(t), diff(x__2(t),t) = -2*x__1(t)+2*x__2(t), x__1(0) = 0, x__2(0) = 5],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = 3 \,{\mathrm e}^{-t}-3 \,{\mathrm e}^{4 t} \] \[ x_{2} \relax (t ) = 2 \,{\mathrm e}^{-t}+3 \,{\mathrm e}^{4 t} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 37
DSolve[{x1'[t]==1*x1[t]-3*x2[t],x2'[t]==-2*x1[t]+2*x2[t]},{x1[0]==0,x2[0]==5},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to -3 e^{-t} \left (e^{5 t}-1\right ) \\ \text {x2}(t)\to e^{-t} \left (3 e^{5 t}+2\right ) \\ \end{align*}