9.6.5 problem problem 5

Internal problem ID [1012]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number : problem 5
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 )&=7 x_{1} \left (t \right )+x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-4 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

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

dsolve([diff(x__1(t),t)=7*x__1(t)+1*x__2(t),diff(x__2(t),t)=-4*x__1(t)+3*x__2(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 45

DSolve[{D[ x1[t],t]==7*x1[t]+1*x2[t],D[ x2[t],t]==-4*x1[t]+3*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to e^{5 t} (2 c_1 t+c_2 t+c_1) \\ \text {x2}(t)\to e^{5 t} (c_2-2 (2 c_1+c_2) t) \\ \end{align*}