9.6.4 problem problem 4

Internal problem ID [1011]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number : problem 4
Date solved : Monday, January 27, 2025 at 03:22:54 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{1} \left (t \right )+5 x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 29

dsolve([diff(x__1(t),t)=3*x__1(t)-1*x__2(t),diff(x__2(t),t)=1*x__1(t)+5*x__2(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{4 t} \left (c_2 t +c_1 \right ) \\ x_{2} \left (t \right ) &= -{\mathrm e}^{4 t} \left (c_2 t +c_1 +c_2 \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 42

DSolve[{D[ x1[t],t]==3*x1[t]-1*x2[t],D[ x2[t],t]==1*x1[t]+5*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to -e^{4 t} (c_1 (t-1)+c_2 t) \\ \text {x2}(t)\to e^{4 t} ((c_1+c_2) t+c_2) \\ \end{align*}