9.3.2 problem problem 14

Internal problem ID [964]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 7.2, Matrices and Linear systems. Page 384
Problem number : problem 14
Date solved : Monday, January 27, 2025 at 03:22:38 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=-3 x_{1} \left (t \right )+2 x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=-3 x_{1} \left (t \right )+4 x_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 35

dsolve([diff(x__1(t),t)=-3*x__1(t)+2*x__2(t),diff(x__2(t),t)=-3*x__1(t)+4*x__2(t)],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 73

DSolve[{D[ x1[t],t]==-3*x1[t]+2*x2[t],D[ x2[t],t]==-3*x1[t]+4*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to \frac {1}{5} e^{-2 t} \left (2 c_2 \left (e^{5 t}-1\right )-c_1 \left (e^{5 t}-6\right )\right ) \\ \text {x2}(t)\to \frac {1}{5} e^{-2 t} \left (c_2 \left (6 e^{5 t}-1\right )-3 c_1 \left (e^{5 t}-1\right )\right ) \\ \end{align*}