Internal problem ID [5780]
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 }\relax (t )&=3 x \relax (t )+2 y \relax (t )\\ y^{\prime }\relax (t )&=-2 x \relax (t )-y \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.093 (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)
\[ x \relax (t ) = -\frac {{\mathrm e}^{t} \left (2 t c_{2}+2 c_{1}+c_{2}\right )}{2} \] \[ y \relax (t ) = \left (t c_{2}+c_{1}\right ) {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.004 (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*}