Internal problem ID [6367]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 76.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=2 x \relax (t )+y \relax (t )-z \relax (t )\\ y^{\prime }\relax (t )&=-x \relax (t )+2 z \relax (t )\\ z^{\prime }\relax (t )&=-x \relax (t )-2 y \relax (t )+4 z \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 59
dsolve([diff(x(t),t)=2*x(t)+y(t)-z(t),diff(y(t),t)=-x(t)+2*z(t),diff(z(t),t)=-x(t)-2*y(t)+4*z(t)],[x(t), y(t), z(t)], singsol=all)
\[ x \relax (t ) = -{\mathrm e}^{2 t} \left (2 t c_{3}+c_{2}-4 c_{3}\right ) \] \[ y \relax (t ) = {\mathrm e}^{2 t} \left (t^{2} c_{3}+t c_{2}+c_{1}-2 c_{3}\right ) \] \[ z \relax (t ) = {\mathrm e}^{2 t} \left (t^{2} c_{3}+t c_{2}+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 94
DSolve[{x'[t]== 2*x[t]+y[t]-z[t],y'[t] == -x[t]+2*z[t],z'[t]==-x[t]-2*y[t]+4*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{2 t} ((c_2-c_3) t+c_1) \\ y(t)\to \frac {1}{2} e^{2 t} (-2 c_1 t-(c_2-c_3) t (t+4)+2 c_2) \\ z(t)\to \frac {1}{2} e^{2 t} (-2 c_1 t-c_2 t (t+4)+c_3 (t (t+4)+2)) \\ \end{align*}