Internal problem ID [7117]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 73.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right )+5 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve([diff(x(t),t) = x(t)-2*y(t), diff(y(t),t) = 2*x(t)+5*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{3 t} \left (c_{2} t +c_{1} \right ) \\ y \left (t \right ) &= -\frac {{\mathrm e}^{3 t} \left (2 c_{2} t +2 c_{1} +c_{2} \right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 46
DSolve[{x'[t]== x[t]-2*y[t],y'[t] == 2*x[t]+5*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -e^{3 t} (c_1 (2 t-1)+2 c_2 t) \\ y(t)\to e^{3 t} (2 (c_1+c_2) t+c_2) \\ \end{align*}