Internal problem ID [10232]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1900.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=4 x \left (t \right )\\ y^{\prime }\left (t \right )&=x \left (t \right )-2 y \left (t \right )\\ z^{\prime }\left (t \right )&=x \left (t \right )-4 y \left (t \right )+z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.329 (sec). Leaf size: 50
dsolve([diff(x(t),t)=4*x(t),diff(y(t),t)=x(t)-2*y(t),diff(z(t),t)=x(t)-4*y(t)+z(t)],[x(t), y(t), z(t)], singsol=all)
\[ x \left (t \right ) = 9 c_{1} {\mathrm e}^{4 t} \] \[ y \left (t \right ) = \frac {3 c_{1} {\mathrm e}^{4 t}}{2}+\frac {3 c_{2} {\mathrm e}^{-2 t}}{4} \] \[ z \left (t \right ) = c_{1} {\mathrm e}^{4 t}+c_{2} {\mathrm e}^{-2 t}+c_{3} {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 88
DSolve[{x'[t]==4*x[t],y'[t]==x[t]-2*y[t],z'[t]==x[t]-4*y[t]+z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{4 t} y(t)\to \frac {1}{6} e^{-2 t} \left (c_1 \left (e^{6 t}-1\right )+6 c_2\right ) z(t)\to \frac {1}{9} e^{-2 t} \left (c_1 \left (e^{3 t}+e^{6 t}-2\right )-12 c_2 \left (e^{3 t}-1\right )+9 c_3 e^{3 t}\right ) \end{align*}