Internal problem ID [1830]
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: 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1} \relax (t )+x_{2} \relax (t )\\ x_{2}^{\prime }\relax (t )&=4 x_{1} \relax (t )+x_{2} \relax (t ) \end {align*}
With initial conditions \[ [x_{1} \relax (0) = 2, x_{2} \relax (0) = 3] \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 34
dsolve([diff(x__1(t),t) = x__1(t)+x__2(t), diff(x__2(t),t) = 4*x__1(t)+x__2(t), x__1(0) = 2, x__2(0) = 3],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = \frac {{\mathrm e}^{-t}}{4}+\frac {7 \,{\mathrm e}^{3 t}}{4} \] \[ x_{2} \relax (t ) = -\frac {{\mathrm e}^{-t}}{2}+\frac {7 \,{\mathrm e}^{3 t}}{2} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 43
DSolve[{x1'[t]==1*x1[t]+1*x2[t],x2'[t]==4*x1[t]+1*x2[t]},{x1[0]==2,x2[0]==3},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{4} e^{-t} \left (7 e^{4 t}+1\right ) \\ \text {x2}(t)\to e^t (4 \sinh (2 t)+3 \cosh (2 t)) \\ \end{align*}