Internal problem ID [2272]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 26, page 115
Problem number: 12.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right )+3 y \left (t \right )\\ z^{\prime }\left (t \right )&=3 y \left (t \right )-2 z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 53
dsolve([diff(x(t),t)=3*x(t),diff(y(t),t)=2*x(t)+3*y(t),diff(z(t),t)=3*y(t)-2*z(t)],[x(t), y(t), z(t)], singsol=all)
\begin{align*} x \left (t \right ) = \frac {5 c_{3} {\mathrm e}^{3 t}}{6} y \left (t \right ) = \frac {{\mathrm e}^{3 t} \left (5 c_{3} t +5 c_{2} +c_{3} \right )}{3} z \left (t \right ) = {\mathrm e}^{-2 t} c_{1} +c_{2} {\mathrm e}^{3 t}+c_{3} {\mathrm e}^{3 t} t \end{align*}
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 78
DSolve[{x'[t]==3*x[t],y'[t]==2*x[t]+3*y[t],z'[t]==3*y[t]-2*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to c_1 e^{3 t} y(t)\to e^{3 t} (2 c_1 t+c_2) z(t)\to \frac {1}{25} e^{-2 t} \left (6 c_1 \left (e^{5 t} (5 t-1)+1\right )+5 \left (3 c_2 \left (e^{5 t}-1\right )+5 c_3\right )\right ) \end{align*}