7.25.7 problem 7

Internal problem ID [627]
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 : 7
Date solved : Monday, January 27, 2025 at 02:56:29 AM
CAS classification : system_of_ODEs

\begin{align*} x_{1}^{\prime }\left (t \right )&=-3 x_{1} \left (t \right )+4 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=6 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 30

dsolve([diff(x__1(t),t)=-3*x__1(t)+4*x__2(t),diff(x__2(t),t)=6*x__1(t)-5*x__2(t)],singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{t} c_1 +c_2 \,{\mathrm e}^{-9 t} \\ x_{2} \left (t \right ) &= {\mathrm e}^{t} c_1 -\frac {3 c_2 \,{\mathrm e}^{-9 t}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 74

DSolve[{D[x1[t],t]==-3*x1[t]+4*x2[t],D[x2[t],t]==6*x1[t]-5*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to \frac {1}{5} e^{-9 t} \left (c_1 \left (3 e^{10 t}+2\right )+2 c_2 \left (e^{10 t}-1\right )\right ) \\ \text {x2}(t)\to \frac {1}{5} e^{-9 t} \left (3 c_1 \left (e^{10 t}-1\right )+c_2 \left (2 e^{10 t}+3\right )\right ) \\ \end{align*}