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 }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+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: 0.016 (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], singsol=all)
\begin{align*} x_{1} \left (t \right ) &= \frac {7 \,{\mathrm e}^{3 t}}{4}+\frac {{\mathrm e}^{-t}}{4} \\ x_{2} \left (t \right ) &= \frac {7 \,{\mathrm e}^{3 t}}{2}-\frac {{\mathrm e}^{-t}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 44
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 \frac {1}{2} e^{-t} \left (7 e^{4 t}-1\right ) \\ \end{align*}