Internal problem ID [6362]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 71.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=9 x \relax (t )+4 y \relax (t )\\ y^{\prime }\relax (t )&=-6 x \relax (t )-y \relax (t )\\ z^{\prime }\relax (t )&=6 x \relax (t )+4 y \relax (t )+3 z \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.235 (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)
\[ x \relax (t ) = c_{2} {\mathrm e}^{5 t}+\frac {2 c_{3} {\mathrm e}^{3 t}}{3}-\frac {2 c_{1} {\mathrm e}^{3 t}}{3} \] \[ y \relax (t ) = -c_{2} {\mathrm e}^{5 t}-c_{3} {\mathrm e}^{3 t}+c_{1} {\mathrm e}^{3 t} \] \[ z \relax (t ) = c_{2} {\mathrm e}^{5 t}+c_{3} {\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 95
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^{4 t} (c_1 \cosh (t)+(5 c_1+4 c_2) \sinh (t)) \\ y(t)\to 3 (c_1+c_2) e^{3 t}-(3 c_1+2 c_2) e^{5 t} \\ 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*}