Internal problem ID [10231]
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 }\left (t \right )&=2 x \left (t \right )\\ y^{\prime }\left (t \right )&=3 x \left (t \right )-2 y \left (t \right )\\ z^{\prime }\left (t \right )&=2 y \left (t \right )+3 z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.265 (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)
\[ x \left (t \right ) = -\frac {2 c_{3} {\mathrm e}^{2 t}}{3} \] \[ y \left (t \right ) = -\frac {5 c_{2} {\mathrm e}^{-2 t}}{2}-\frac {c_{3} {\mathrm e}^{2 t}}{2} \] \[ z \left (t \right ) = c_{1} {\mathrm e}^{3 t}+c_{2} {\mathrm e}^{-2 t}+c_{3} {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 93
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 \frac {1}{4} e^{-2 t} \left (3 c_1 \left (e^{4 t}-1\right )+4 c_2\right ) z(t)\to \frac {1}{10} e^{-2 t} \left (c_1 \left (-15 e^{4 t}+12 e^{5 t}+3\right )+4 c_2 \left (e^{5 t}-1\right )+10 c_3 e^{5 t}\right ) \end{align*}