28.4.46 problem 7.46

Internal problem ID [4578]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 7. Systems of linear differential equations. Problems at page 351
Problem number : 7.46
Date solved : Monday, January 27, 2025 at 09:23:44 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.042 (sec). Leaf size: 41

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

\begin{align*} x_{1} \left (t \right ) &= \frac {{\mathrm e}^{t} \left (2 c_{1} t +4 t^{2}+c_{1} +2 c_{2} +4 t \right )}{4} \\ x_{2} \left (t \right ) &= {\mathrm e}^{t} \left (c_{1} t +2 t^{2}+c_{2} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 51

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

\begin{align*} \text {x1}(t)\to e^t \left (t^2+t+2 c_1 t-c_2 t+c_1\right ) \\ \text {x2}(t)\to e^t \left (2 t^2+4 c_1 t-2 c_2 t+c_2\right ) \\ \end{align*}