Internal problem ID [5911]
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 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )-8\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )+3 \end {align*}
With initial conditions \[ [x_{1} \left (0\right ) = 1, x_{2} \left (0\right ) = 2] \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
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(0) = 1, x__2(0) = 2], singsol=all)
\begin{align*} x_{1} \left (t \right ) &= \frac {{\mathrm e}^{2 t}}{4}-\frac {11 t}{2}+\frac {3}{4} \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{2 t}}{4}+\frac {7}{4}+\frac {11 t}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 36
DSolve[{x1'[t]==x1[t]+x2[t]-8,x2'[t]==x1[t]+x2[t]+3},{x1[0]==1,x2[0]==2},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{4} \left (-22 t+e^{2 t}+3\right ) \\ \text {x2}(t)\to \frac {1}{4} \left (22 t+e^{2 t}+7\right ) \\ \end{align*}