Internal problem ID [5157]
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 5.15 part 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1}\relax (t )+x_{2}\relax (t )-8\\ x_{2}^{\prime }\relax (t )&=x_{1}\relax (t )+x_{2}\relax (t )+3 \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 35
dsolve([diff(x__1(t),t)=x__1(t)+x__2(t)-8,diff(x__2(t),t)=x__1(t)+x__2(t)+3],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {c_{1} {\mathrm e}^{2 t}}{2}+\frac {5}{2}-\frac {11 t}{2}-c_{2} \] \[ x_{2}\relax (t ) = \frac {c_{1} {\mathrm e}^{2 t}}{2}+\frac {11 t}{2}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 66
DSolve[{x1'[t]==x1[t]+x2[t]-8,x2'[t]==x1[t]+x2[t]+3},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{4} \left (-22 t+2 (c_1+c_2) e^{2 t}+5+2 c_1-2 c_2\right ) \\ \text {x2}(t)\to \frac {1}{4} \left (22 t+2 (c_1+c_2) e^{2 t}+5-2 c_1+2 c_2\right ) \\ \end{align*}