Internal problem ID [6525]
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 10.3 Homogeneous Linear
Systems with Constant Coefficients. Page 387
Problem number: 1(f).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-4 x \left (t \right )-y \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )-2 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 32
dsolve([diff(x(t),t)=-4*x(t)-y(t),diff(y(t),t)=x(t)-2*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -{\mathrm e}^{-3 t} \left (c_{2} t +c_{1} -c_{2} \right ) \] \[ y \left (t \right ) = {\mathrm e}^{-3 t} \left (c_{2} t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 43
DSolve[{x'[t]==-4*x[t]-y[t],y'[t]==x[t]-2*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-3 t} (c_1 (-t)-c_2 t+c_1) y(t)\to e^{-3 t} ((c_1+c_2) t+c_2) \end{align*}