48.5.7 problem Problem 5.8

Internal problem ID [7572]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 5. Systems of First Order Differential Equations. Section 5.11 Problems. Page 360
Problem number : Problem 5.8
Date solved : Monday, January 27, 2025 at 03:06:26 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=3 x_{1} \left (t \right )-x_{2} \left (t \right )\\ \frac {d}{d t}x_{2} \left (t \right )&=16 x_{1} \left (t \right )-5 x_{2} \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) = 1\\ x_{2} \left (0\right ) = 1 \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 27

dsolve([diff(x__1(t),t) = 3*x__1(t)-x__2(t), diff(x__2(t),t) = 16*x__1(t)-5*x__2(t), x__1(0) = 1, x__2(0) = 1], singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-t} \left (3 t +1\right ) \\ x_{2} \left (t \right ) &= {\mathrm e}^{-t} \left (12 t +1\right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

DSolve[{D[ x1[t],t]==3*x1[t]-x2[t],D[ x2[t],t]==16*x1[t]-5*x2[t]},{x1[0]==1,x2[0]==1},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to e^{-t} (3 t+1) \\ \text {x2}(t)\to e^{-t} (12 t+1) \\ \end{align*}