Internal problem ID [7490]
Book: Second order enumerated odes
Section: section 2
Problem number: 49.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )+y \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right )+y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 32
dsolve([diff(x(t),t)=3*x(t)+y(t),diff(y(t),t)=-x(t)+y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{2 t} \left (c_{2} t +c_{1} \right ) \\ y \left (t \right ) &= -{\mathrm e}^{2 t} \left (c_{2} t +c_{1} -c_{2} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 42
DSolve[{x'[t]==3*x[t]+y[t],y'[t]==-x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{2 t} (c_1 (t+1)+c_2 t) \\ y(t)\to e^{2 t} (c_2-(c_1+c_2) t) \\ \end{align*}