Internal problem ID [5899]
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 5.2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+3 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )+3 x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 36
dsolve([diff(x__1(t),t)=x__1(t)+3*x__2(t),diff(x__2(t),t)=5*x__1(t)+3*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \left (t \right ) = \frac {3 c_{1} {\mathrm e}^{6 t}}{5}-{\mathrm e}^{-2 t} c_{2} \] \[ x_{2} \left (t \right ) = c_{1} {\mathrm e}^{6 t}+{\mathrm e}^{-2 t} c_{2} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 74
DSolve[{x1'[t]==x1[t]+3*x2[t],x2'[t]==5*x1[t]+3*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{8} e^{-2 t} \left (c_1 \left (3 e^{8 t}+5\right )+3 c_2 \left (e^{8 t}-1\right )\right ) \text {x2}(t)\to \frac {1}{8} e^{-2 t} \left (5 c_1 \left (e^{8 t}-1\right )+c_2 \left (5 e^{8 t}+3\right )\right ) \end{align*}