48.5.3 problem Problem 5.3

Internal problem ID [7568]
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 5.3
Date solved : Monday, January 27, 2025 at 03:06:22 PM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 28

dsolve([diff(x__1(t),t) = -x__1(t)+3*x__2(t), diff(x__2(t),t) = -3*x__1(t)+5*x__2(t), x__1(0) = 1, x__2(0) = 2], singsol=all)
 

\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{2 t} \left (3 t +1\right ) \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{2 t} \left (9 t +6\right )}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 30

DSolve[{D[ x1[t],t]==-x1[t]+3*x2[t],D[ x2[t],t]==-3*x1[t]+5*x2[t]},{x1[0]==1,x2[0]==2},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {x1}(t)\to e^{2 t} (3 t+1) \\ \text {x2}(t)\to e^{2 t} (3 t+2) \\ \end{align*}