Internal problem ID [5146]
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 }\relax (t )&=x_{1}\relax (t )+3 x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=5 x_{1}\relax (t )+3 x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.051 (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)
\[ x_{1}\relax (t ) = -{\mathrm e}^{-2 t} c_{1}+\frac {3 c_{2} {\mathrm e}^{6 t}}{5} \] \[ x_{2}\relax (t ) = {\mathrm e}^{-2 t} c_{1}+c_{2} {\mathrm e}^{6 t} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 68
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 (3 (c_1+c_2) e^{8 t}+5 c_1-3 c_2\right ) \\ \text {x2}(t)\to \frac {1}{8} e^{-2 t} \left (5 (c_1+c_2) e^{8 t}-5 c_1+3 c_2\right ) \\ \end{align*}