Internal problem ID [5152]
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 5.9.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1}\relax (t )-2 x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=3 x_{1}\relax (t )-4 x_{2}\relax (t ) \end {align*}
With initial conditions \[ [x_{1}\relax (0) = 1, x_{2}\relax (0) = 0] \]
✓ Solution by Maple
Time used: 0.053 (sec). Leaf size: 34
dsolve([diff(x__1(t),t) = x__1(t)-2*x__2(t), diff(x__2(t),t) = 3*x__1(t)-4*x__2(t), x__1(0) = 1, x__2(0) = 0],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = -2 \,{\mathrm e}^{-2 t}+3 \,{\mathrm e}^{-t} \] \[ x_{2}\relax (t ) = -3 \,{\mathrm e}^{-2 t}+3 \,{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 33
DSolve[{x1'[t]==x1[t]-2*x2[t],x2'[t]==3*x1[t]-4*x2[t]},{x1[0]==1,x2[0]==0},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{-2 t} \left (3 e^t-2\right ) \\ \text {x2}(t)\to 3 e^{-2 t} \left (e^t-1\right ) \\ \end{align*}