7.25.5 problem 5

Internal problem ID [625]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 5. Linear systems of differential equations. Section 5.4 (The eigenvalue method for homogeneous systems). Problems at page 378
Problem number : 5
Date solved : Monday, January 27, 2025 at 02:56:28 AM
CAS classification : system_of_ODEs

\begin{align*} x_{1}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )-7 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 34

dsolve([diff(x__1(t),t)=6*x__1(t)-7*x__2(t),diff(x__2(t),t)=x__1(t)-2*x__2(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= c_1 \,{\mathrm e}^{5 t}+c_2 \,{\mathrm e}^{-t} \\ x_{2} \left (t \right ) &= \frac {c_1 \,{\mathrm e}^{5 t}}{7}+c_2 \,{\mathrm e}^{-t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 72

DSolve[{D[x1[t],t]==6*x1[t]-7*x2[t],D[x2[t],t]==x1[t]-2*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to \frac {1}{6} e^{-t} \left (c_1 \left (7 e^{6 t}-1\right )-7 c_2 \left (e^{6 t}-1\right )\right ) \\ \text {x2}(t)\to \frac {1}{6} e^{-t} \left (c_1 \left (e^{6 t}-1\right )-c_2 \left (e^{6 t}-7\right )\right ) \\ \end{align*}