Internal problem ID [5901]
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 5.4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )-x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=5 x_{1} \left (t \right )+2 x_{2} \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 61
dsolve([diff(x__1(t),t)=4*x__1(t)-x__2(t),diff(x__2(t),t)=5*x__1(t)+2*x__2(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{3 t} \left (c_{1} \sin \left (2 t \right )+c_{2} \cos \left (2 t \right )\right ) \\ x_{2} \left (t \right ) &= -{\mathrm e}^{3 t} \left (2 c_{1} \cos \left (2 t \right )-c_{2} \cos \left (2 t \right )-c_{1} \sin \left (2 t \right )-2 c_{2} \sin \left (2 t \right )\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 70
DSolve[{x1'[t]==4*x1[t]-x2[t],x2'[t]==5*x1[t]+2*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{2} e^{3 t} (2 c_1 \cos (2 t)+(c_1-c_2) \sin (2 t)) \\ \text {x2}(t)\to \frac {1}{2} e^{3 t} (2 c_2 \cos (2 t)+(5 c_1-c_2) \sin (2 t)) \\ \end{align*}