9.6.6 problem problem 6

Internal problem ID [1013]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 7.6, Multiple Eigenvalue Solutions. Page 451
Problem number : problem 6
Date solved : Monday, January 27, 2025 at 03:22:55 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=x_{1} \left (t \right )-4 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=4 x_{1} \left (t \right )+9 x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 32

dsolve([diff(x__1(t),t)=1*x__1(t)-4*x__2(t),diff(x__2(t),t)=4*x__1(t)+9*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 ) &= -\frac {{\mathrm e}^{5 t} \left (4 c_2 t +4 c_1 +c_2 \right )}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 46

DSolve[{D[ x1[t],t]==1*x1[t]-4*x2[t],D[ x2[t],t]==4*x1[t]+9*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to -e^{5 t} (c_1 (4 t-1)+4 c_2 t) \\ \text {x2}(t)\to e^{5 t} (4 (c_1+c_2) t+c_2) \\ \end{align*}