Internal problem ID [5147]
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 5.3.
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 )&=-3 x_{1} \relax (t )+5 x_{2} \relax (t ) \end {align*}
With initial conditions \[ [x_{1} \relax (0) = 1, x_{2} \relax (0) = 2] \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 29
dsolve([diff(x__1(t),t) = -x__1(t)+3*x__2(t), diff(x__2(t),t) = -3*x__1(t)+5*x__2(t), x__1(0) = 1, x__2(0) = 2],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = \frac {{\mathrm e}^{2 t} \left (9 t +3\right )}{3} \] \[ x_{2} \relax (t ) = {\mathrm e}^{2 t} \left (3 t +2\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 30
DSolve[{x1'[t]==-x1[t]+3*x2[t],x2'[t]==-3*x1[t]+5*x2[t]},{x1[0]==1,x2[0]==2},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{2 t} (3 t+1) \\ \text {x2}(t)\to e^{2 t} (3 t+2) \\ \end{align*}