Internal problem ID [13078]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Exercises section 3.2. page 277
Problem number: 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-5 x \left (t \right )-2 y\\ y^{\prime }&=-x \left (t \right )-4 y \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 36
dsolve([diff(x(t),t)=-5*x(t)-2*y(t),diff(y(t),t)=-x(t)-4*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-6 t} c_{1} +c_{2} {\mathrm e}^{-3 t} \\ y \left (t \right ) &= \frac {{\mathrm e}^{-6 t} c_{1}}{2}-c_{2} {\mathrm e}^{-3 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 71
DSolve[{x'[t]==-5*x[t]-2*y[t],y'[t]==-x[t]-4*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-6 t} \left (c_1 \left (e^{3 t}+2\right )-2 c_2 \left (e^{3 t}-1\right )\right ) \\ y(t)\to \frac {1}{3} e^{-6 t} \left (c_1 \left (-e^{3 t}\right )+2 c_2 e^{3 t}+c_1+c_2\right ) \\ \end{align*}