Internal problem ID [15525]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 3 (Systems of differential equations). Section 22. Integration of homogeneous
linear systems with constant coefficients. Eulers method. Exercises page 230
Problem number: 802.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=8 y \left (t \right )-x \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 36
dsolve([diff(x(t),t)=8*y(t)-x(t),diff(y(t),t)=x(t)+y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{-3 t} \\ y \left (t \right ) &= \frac {c_{1} {\mathrm e}^{3 t}}{2}-\frac {c_{2} {\mathrm e}^{-3 t}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 72
DSolve[{x'[t]==8*y[t]-x[t],y'[t]==x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{3} e^{-3 t} \left (c_1 \left (e^{6 t}+2\right )+4 c_2 \left (e^{6 t}-1\right )\right ) \\ y(t)\to \frac {1}{6} e^{-3 t} \left (c_1 \left (e^{6 t}-1\right )+2 c_2 \left (2 e^{6 t}+1\right )\right ) \\ \end{align*}