Internal problem ID [6363]
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: 0.031 (sec). Leaf size: 35
dsolve([diff(x(t),t) = x(t)-2*y(t), diff(y(t),t) = 2*x(t)+5*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -\frac {{\mathrm e}^{3 t} \left (2 c_{2} t +2 c_{1} -c_{2} \right )}{2} \] \[ y \left (t \right ) = {\mathrm e}^{3 t} \left (c_{2} t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 44
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} (-2 c_1 t-2 c_2 t+c_1) \\ y(t)\to e^{3 t} (2 (c_1+c_2) t+c_2) \\ \end{align*}