Internal problem ID [9486]
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 }\relax (t )&=-3 x \relax (t )+48 y \relax (t )-28 z \relax (t )\\ y^{\prime }\relax (t )&=-4 x \relax (t )+40 y \relax (t )-22 z \relax (t )\\ z^{\prime }\relax (t )&=-6 x \relax (t )+57 y \relax (t )-31 z \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.187 (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)},{x(t), y(t), z(t)}, singsol=all)
\[ x \relax (t ) = c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{2 t}+c_{3} {\mathrm e}^{3 t} \] \[ y \relax (t ) = \frac {2 c_{1} {\mathrm e}^{t}}{3}+\frac {c_{2} {\mathrm e}^{2 t}}{4}+c_{3} {\mathrm e}^{3 t} \] \[ z \relax (t ) = c_{1} {\mathrm e}^{t}+\frac {c_{2} {\mathrm e}^{2 t}}{4}+\frac {3 c_{3} {\mathrm e}^{3 t}}{2} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 156
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 ((3 c_2-2 c_3) e^t-2 (c_1-9 c_2+5 c_3) e^{2 t}+2 (c_1-10 c_2+6 c_3)\right ) \\ z(t)\to e^t \left ((3 c_2-2 c_3) e^t-3 (c_1-9 c_2+5 c_3) e^{2 t}+3 (c_1-10 c_2+6 c_3)\right ) \\ \end{align*}