Internal problem ID [12544]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 10. Applications of Systems of Equations. Exercises 10.2 page 432
Problem number: 8.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )-2 y \left (t \right )-6\\ y^{\prime }\left (t \right )&=4 x \left (t \right )-y \left (t \right )+2 \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 60
dsolve([diff(x(t),t)=3*x(t)-2*y(t)-6,diff(y(t),t)=4*x(t)-1*y(t)+2],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -2-\frac {{\mathrm e}^{t} \left (\sin \left (2 t \right ) c_{1} -\sin \left (2 t \right ) c_{2} -\cos \left (2 t \right ) c_{1} -\cos \left (2 t \right ) c_{2} \right )}{2} \] \[ y \left (t \right ) = -6+{\mathrm e}^{t} \left (\sin \left (2 t \right ) c_{2} +\cos \left (2 t \right ) c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.358 (sec). Leaf size: 64
DSolve[{x'[t]==3*x[t]-2*y[t]-6,y'[t]==4*x[t]-1*y[t]+2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^t \cos (2 t)+(c_1-c_2) e^t \sin (2 t)-2 y(t)\to c_2 e^t \cos (2 t)+(2 c_1-c_2) e^t \sin (2 t)-6 \end{align*}