Internal problem ID [5150]
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 5.7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-2 x_{1}\relax (t )+x_{2}\relax (t )+2 \,{\mathrm e}^{-t}\\ x_{2}^{\prime }\relax (t )&=x_{1}\relax (t )-2 x_{2}\relax (t )+3 t \end {align*}
✓ Solution by Maple
Time used: 0.098 (sec). Leaf size: 65
dsolve([diff(x__1(t),t)=-2*x__1(t)+x__2(t)+2*exp(-t),diff(x__2(t),t)=x__1(t)-2*x__2(t)+3*t],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = -c_{2} {\mathrm e}^{-3 t}+{\mathrm e}^{-t} c_{1}+\frac {{\mathrm e}^{-t}}{2}-\frac {4}{3}+t \,{\mathrm e}^{-t}+t \] \[ x_{2}\relax (t ) = c_{2} {\mathrm e}^{-3 t}+{\mathrm e}^{-t} c_{1}-\frac {{\mathrm e}^{-t}}{2}-\frac {5}{3}+2 t +t \,{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 90
DSolve[{x1'[t]==-2*x1[t]+x2[t]+2*Exp[-t],x2'[t]==x1[t]-2*x2[t]+3*t},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to t+\frac {1}{2} e^{-3 t} \left (e^{2 t} (2 t+1+c_1+c_2)+c_1-c_2\right )-\frac {4}{3} \\ \text {x2}(t)\to \frac {1}{6} e^{-3 t} \left (2 e^{3 t} (6 t-5)+3 e^{2 t} (2 t-1+c_1+c_2)-3 c_1+3 c_2\right ) \\ \end{align*}