Internal problem ID [7119]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 75.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right )\\ y^{\prime }\left (t \right )&=y \left (t \right )\\ z^{\prime }\left (t \right )&=z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve([diff(x(t),t)=x(t)+y(t),diff(y(t),t)=y(t),diff(z(t),t)=z(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{t} \left (c_{2} t +c_{1} \right ) \\ y \left (t \right ) &= c_{2} {\mathrm e}^{t} \\ z \left (t \right ) &= c_{3} {\mathrm e}^{t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 62
DSolve[{x'[t]== x[t]+y[t],y'[t] == y[t],z'[t]==z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t (c_2 t+c_1) \\ y(t)\to c_2 e^t \\ z(t)\to c_3 e^t \\ x(t)\to e^t (c_2 t+c_1) \\ y(t)\to c_2 e^t \\ z(t)\to 0 \\ \end{align*}