Internal problem ID [5148]
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 }\relax (t )&=4 x_{1}\relax (t )-x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=5 x_{1}\relax (t )+2 x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.054 (sec). Leaf size: 59
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)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {{\mathrm e}^{3 t} \left (\sin \left (2 t \right ) c_{1}-2 \sin \left (2 t \right ) c_{2}+2 \cos \left (2 t \right ) c_{1}+\cos \left (2 t \right ) c_{2}\right )}{5} \] \[ x_{2}\relax (t ) = {\mathrm e}^{3 t} \left (\sin \left (2 t \right ) c_{1}+\cos \left (2 t \right ) c_{2}\right ) \]
✓ 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*}