Internal problem ID [7115]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 71.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=9 x \left (t \right )+4 y \left (t \right )\\ y^{\prime }\left (t \right )&=-6 x \left (t \right )-y \left (t \right )\\ z^{\prime }\left (t \right )&=6 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 66
dsolve([diff(x(t),t)=9*x(t)+4*y(t),diff(y(t),t)=-6*x(t)-y(t),diff(z(t),t)=6*x(t)+4*y(t)+3*z(t)],[x(t), y(t), z(t)], singsol=all)
\[ x \left (t \right ) = c_{2} {\mathrm e}^{5 t}+\frac {2 c_{3} {\mathrm e}^{3 t}}{3}-\frac {2 c_{1} {\mathrm e}^{3 t}}{3} \] \[ y \left (t \right ) = -c_{2} {\mathrm e}^{5 t}-c_{3} {\mathrm e}^{3 t}+c_{1} {\mathrm e}^{3 t} \] \[ z \left (t \right ) = c_{2} {\mathrm e}^{5 t}+c_{3} {\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 103
DSolve[{x'[t]==9*x[t]+4*y[t],y'[t]==-6*x[t]-y[t],z'[t]==6*x[t]+4*y[t]+3*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{3 t} \left (c_1 \left (3 e^{2 t}-2\right )+2 c_2 \left (e^{2 t}-1\right )\right ) y(t)\to -e^{3 t} \left (3 c_1 \left (e^{2 t}-1\right )+c_2 \left (2 e^{2 t}-3\right )\right ) z(t)\to e^{3 t} \left (3 c_1 \left (e^{2 t}-1\right )+2 c_2 \left (e^{2 t}-1\right )+c_3\right ) \end{align*}