Internal problem ID [6533]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 10. Systems of First-Order Equations. Section A. Drill exercises. Page
400
Problem number: 3(a).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )+2 y \left (t \right )\\ y^{\prime }\left (t \right )&=-2 x \left (t \right )-y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 29
dsolve([diff(x(t),t)=3*x(t)+2*y(t),diff(y(t),t)=-2*x(t)-y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -\frac {{\mathrm e}^{t} \left (2 c_{2} t +2 c_{1} +c_{2} \right )}{2} \] \[ y \left (t \right ) = \left (c_{2} t +c_{1} \right ) {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 40
DSolve[{x'[t]==3*x[t]+2*y[t],y'[t]==-2*x[t]-y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t (2 c_1 t+2 c_2 t+c_1) y(t)\to e^t (c_2-2 (c_1+c_2) t) \end{align*}