Internal problem ID [5908]
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 5.12.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )-18 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-9 x_{2} \left (t \right ) \end {align*}
With initial conditions \[ [x_{1} \left (0\right ) = 2, x_{2} \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve([diff(x__1(t),t) = 3*x__1(t)-18*x__2(t), diff(x__2(t),t) = 2*x__1(t)-9*x__2(t), x__1(0) = 2, x__2(0) = 1], singsol=all)
\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{-3 t} \left (-6 t +2\right ) \\ x_{2} \left (t \right ) &= \frac {{\mathrm e}^{-3 t} \left (-36 t +18\right )}{18} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 30
DSolve[{x1'[t]==3*x1[t]-18*x2[t],x2'[t]==2*x1[t]-9*x2[t]},{x1[0]==2,x2[0]==1},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{-3 t} (2-6 t) \\ \text {x2}(t)\to e^{-3 t} (1-2 t) \\ \end{align*}