Internal problem ID [10230]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1907.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-3 x \left (t \right )+48 y \left (t \right )-28 z \left (t \right )\\ y^{\prime }\left (t \right )&=-4 x \left (t \right )+40 y \left (t \right )-22 z \left (t \right )\\ z^{\prime }\left (t \right )&=-6 x \left (t \right )+57 y \left (t \right )-31 z \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 66
dsolve([diff(x(t),t)=-3*x(t)+48*y(t)-28*z(t),diff(y(t),t)=-4*x(t)+40*y(t)-22*z(t),diff(z(t),t)=-6*x(t)+57*y(t)-31*z(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{3 t} \\ y \left (t \right ) &= \frac {2 c_{1} {\mathrm e}^{t}}{3}+\frac {c_{2} {\mathrm e}^{2 t}}{4}+c_{3} {\mathrm e}^{3 t} \\ z \left (t \right ) &= c_{1} {\mathrm e}^{t}+\frac {c_{2} {\mathrm e}^{2 t}}{4}+\frac {3 c_{3} {\mathrm e}^{3 t}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 157
DSolve[{x'[t]==-3*x[t]+48*y[t]-28*z[t],y'[t]==-4*x[t]+40*y[t]-22*z[t],z'[t]==-6*x[t]+57*y[t]-31*z[t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t \left (c_1 \left (3-2 e^{2 t}\right )+2 \left (e^t-1\right ) \left (3 c_2 \left (3 e^t+5\right )-c_3 \left (5 e^t+9\right )\right )\right ) \\ y(t)\to e^t \left (-2 c_1 \left (e^{2 t}-1\right )+c_2 \left (3 e^t+18 e^{2 t}-20\right )-2 c_3 \left (e^t+5 e^{2 t}-6\right )\right ) \\ z(t)\to e^t \left (-3 c_1 \left (e^{2 t}-1\right )+3 c_2 \left (e^t+9 e^{2 t}-10\right )-c_3 \left (2 e^t+15 e^{2 t}-18\right )\right ) \\ \end{align*}