Internal problem ID [9478]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1899.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )&=2 x \relax (t )\\ y^{\prime }\relax (t )&=3 x \relax (t )-2 y \relax (t )\\ z^{\prime }\relax (t )&=2 y \relax (t )+3 z \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.099 (sec). Leaf size: 52
dsolve({diff(x(t),t)=2*x(t),diff(y(t),t)=3*x(t)-2*y(t),diff(z(t),t)=2*y(t)+3*z(t)},{x(t), y(t), z(t)}, singsol=all)
\[ x \relax (t ) = c_{3} {\mathrm e}^{2 t} \] \[ y \relax (t ) = \frac {3 c_{3} {\mathrm e}^{2 t}}{4}+c_{2} {\mathrm e}^{-2 t} \] \[ z \relax (t ) = c_{1} {\mathrm e}^{3 t}-\frac {3 c_{3} {\mathrm e}^{2 t}}{2}-\frac {2 c_{2} {\mathrm e}^{-2 t}}{5} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 83
DSolve[{x'[t]==2*x[t],y'[t]==3*x[t]-2*y[t],z'[t]==2*y[t]+3*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{2 t} \\ y(t)\to c_2 e^{-2 t}+3 c_1 \sinh (t) \cosh (t) \\ z(t)\to \frac {1}{10} e^{-2 t} \left (-15 c_1 e^{4 t}+2 (6 c_1+2 c_2+5 c_3) e^{5 t}+3 c_1-4 c_2\right ) \\ \end{align*}